Quantifying Biased Response of Axon to Chemical Gradient

Nov 10, 2014 - Axons are very sensitive to molecular gradients and can discriminate extremely small differences in gradient steepness. Microfluidic de...
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Quantifying Biased Response of Axon to Chemical Gradient Steepness in a Microfluidic Device Rong-Rong Xiao,† Lei Wang,† Lin Zhang,† Yu-Ning Liu,† Xiao-Lei Yu,‡ and Wei-Hua Huang*,† †

Key Laboratory of Analytical Chemistry for Biology and Medicine (Ministry of Education), College of Chemistry and Molecular Sciences, Wuhan University, Wuhan, Hubei 430072, China ‡ School of Physical Sciences and Technology, Wuhan University, Wuhan, Hubei 430072, China S Supporting Information *

ABSTRACT: Axons are very sensitive to molecular gradients and can discriminate extremely small differences in gradient steepness. Microfluidic devices capable of generating chemical gradients and adjusting their steepness could be used to quantify the sensitivity of axonal response. Here, we present a versatile and robust microfluidic device that can generate substrate-bound molecular gradients with evenly varying steepness on a single chip to precisely quantify axonal response. In this device, two solutions are perfused into a central channel via two inlets while partially flowing into two peripheral channels through interconnecting grooves, which gradually decrease the fluid velocity along the central channel. Molecular gradients with evenly and gradually decreased steepness can therefore be generated with a high resolution that is less than 0.05%/mm. In addition, the overall distribution range and resolution of the gradient steepness can be highly and flexibly controlled by adjusting various parameters of the device. Using this device, we quantified the hippocampal axonal response to substrate-bound laminin and ephrin-A5 gradients with varying steepnesses. Our results provided more detailed information on how and to what extent different steepnesses guide hippocampal neuron development during the initial outgrowth. Furthermore, our results show that axons can sensitively respond to very shallow laminin and ephrin-A5 gradients, which could effectively initiate biased differentiation of hippocampal neurons in the steepness range investigated in this study.

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guidance,17−19 cancer metastasis,20−22 and angiogenesis.23,24 Several types of microfluidic devices capable of generating molecular gradients with different steepness have been employed by altering generation conditions such as the flow rate25,26 or driving pressure27−29 of fluids, physical design of the gradient generator,30 and molecular concentrations of inlets17,31 on different chips. However, these studies25−33 could only provide limited information because their gradients formation principles restrict their flexibility in generating molecular gradients with multiple steepnesses and their ability to quantify the sensitivity of axonal response to molecular gradients. In our previous study, we fabricated a microfluidic device with two asymmetrical channels that could simultaneously generate molecular gradients with varying steepnesses in the central channel.9 Using this device, we found that the substrate-bound laminin gradients could accelerate axonal growth and the guidance ratio changed as the gradient steepness varied. However, because of the large difference in velocity caused by the asymmetrical design and opposite flow direction, this device could not generate evenly controlled changes in gradient steepness with high resolution. This limitation restricted our ability to quantify the molecular gradient with subtle changes in

euronal polarity is the process of breaking symmetry to form a long axon and several shorter dendrites in the initial stage of neuronal development.1,2 Long-range and local substrate-anchored guidance cues can direct axon specifications through attractive or repulsive actions;3,4 however, the expression patterns of these gradient-mediated guidance molecules are very complicated. Studies have found that a given molecule can provide different information for guiding neuronal development by generating gradients with varying steepness (s, also called as slope, is defined as the fractional change in concentration of a molecule across 10 μm5). This indicates that gradient steepness is a key factor in axonal pathfinding that directs axons to their appropriate targets.5−9 Local substrate-anchored laminin and ephrin-A5 are two critical guidance molecules expressed in gradients that could guide the formation of topographic maps through attractive and repulsive actions, respectively.10−12 Quantitatively investigating the directions of these two substrate-bound molecular gradients with varying steepness during hippocampal development is significant not only to enhance our understanding of axonal gradient response mechanisms but also to accurately map their expression patterns in vivo. Owing to a flexible design and high gradient resolution,13 various microfluidic gradient generators have emerged as powerful tools for controlling cell gradient microenvironments for investigating many biological questions,14−16 such as axonal © 2014 American Chemical Society

Received: July 20, 2014 Accepted: November 7, 2014 Published: November 10, 2014 11649

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1. All the microfluidic chip masters were fabricated by spincoating with negative photoresist (SU-8 Microchem, U.S.A) on

steepness in directing axonal specification. Axons have high sensitivity in detecting molecular gradient (the lowest s = 0.1%), and extremely small differences (s = 0.06%) in gradient steepness of nerve growth factor (NGF) can trigger a different axonal response.5,8 Therefore, novel microfluidic devices capable of generating chemical gradients with a subtly adjusted steepness should be developed to precisely quantify axon response sensitivity. Here, we present a versatile and robust device with a novel microfluidic architecture format capable of generating substratebound molecular gradients with evenly varying steepness on a single chip in a more highly controlled manner than our previous device. This simple device consists of three main channels (a central channel and two peripheral channels) connected by thin interconnecting grooves. Two solutions are perfused into the central channel via two inlets while partially flowing into two peripheral channels through interconnecting grooves. Flow through the peripheral channels will gradually decrease the fluid velocity along the central channel. Through laminar flow and molecular diffusion, this device can generate molecular gradients with evenly and gradually decreased steepness with a high resolution (less than 0.05%/mm). Using this device, we gained new information on biased axonal responses to substrate-bound laminin and ephrin-A5 gradients with varying steepness. Our results show that both laminin and ephrin-A5 gradients could effectively initiate the biased differentiation of hippocampal neurons. The axonal guidance ratio showed a statistically significant increase when the steepnesses of laminin and ephrin-A5 gradients were greater than 0.5% and 0.1%, respectively. The length of positively extended axons on the laminin gradient showed a statistically significant increase when s > 1%. Within the gradient steepness range investigated in the present study (from 0.02% to 1.31%), ephrin-A5 gradient has no statistically significant effect on the axonal length. As a repulsive factor, ephrin-A5 decreased the amount of neuritis in hippocampal neurons when its average concentration was increased.

Table 1. Dimensions of Microfluidic Chips Used in This Work main channels width/height (μm) device types

peripheral channels

central channel

interconnecting grooves length/ width/height (μm)

C1 C2 C3 C4 C5

1000/100 1000/100 1000/100 1000/100 1000/100

1000/100 1000/100 1000/100 1000/100 1000/100

without 500/25/2 500/25/5 500/50/25 500/100/25

silicon substrates. Briefly, Step 1: The thin interconnecting grooves were patterned by spinning a thinner layer of SU-8 (2005 or 2015) on a cleaned and dried silicon wafer followed by ultraviolet (UV) light exposure through a high-resolution transparency mask (25000 dpi). Step 2: The three main channels were then patterned by spinning a thicker layer (100 μm thick) of SU-8 2100 on the silicon wafer which was patterned with the thinner interconnecting grooves. Step 3: The obtained masters were cured at 160 °C for 30 min to further cross-link the master material on a hot plate. Step 4: The PDMS prepolymer mixture (oligomer/curing agent mass ratio 10:1) was poured over the usable masters which were placed in the suitable Petri dishes. Step 5: After removing bubbles, the PDMS chips were cured at 75 °C for 1.5 h to obtain a cross-linked PDMS replica mold. Fluidic Simulation of Molecular Gradients. A finite element analysis software (COMSOL Multiphysics 4.3) was used to ensure that the designed chips were able to generate the expected molecular gradients. A simpler geometry consisting of three main channels and interconnecting grooves was generated in COMSOL interface first. The simulations presented here used the Navier−Stokes equation for incompressible flow and convection−diffusion equations. As the boundary conditions, a laminar inflow was set at the two inlets and zero pressure was set at the five outlets, no slip on the walls. Mesh density of the entire domain was set to extra fine. A stationary analysis was performed for model calculating. Generation of Substrate-Bound Molecular Gradients. Prior to use, the PDMS devices were rinsed with ethanol to extract uncross-linked PDMS monomers36 and dried at 75 °C. Both the surface of PDMS channel and acid-cleaned glass coverslips were treated with oxygen plasma (Harrick Scientific, Ossining, NY) for 1 min and bound together to form irreversibly sealed microfluidic chips. The poly-L-lysine solution (PLL, 100 μg/mL) was used to fill the PDMS channels immediately, and then, the PDMS chips were stored in an incubator overnight after being sterilized under UV light for 30 min. A PBS solution containing a certain concentration of laminin (50 μg/mL, Sigma, L2020) or recombinant ephrinA5Fc chimera protein (10 μg/mL, R&D Systems, U.S.A) and the other PBS solution containing 5% BSA were perfused through the two inlets of the central channel, respectively, by syringe pumps (Lange, China) at a flow rate of 5 μL/h for 12 h to establish substrate-bound laminin or ephrin-A5 gradients. Microfluidic chips with established substrate-bound gradients were rinsed with PBS and stored in an incubator.

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EXPERIMENTAL SECTION Experiment Reagents. The polydimethylsiloxane (PDMS) prepolymer kit was purchased from Momentive Performance Materials (Waterford, NY). Negative photoresist SU-8 and developer were obtained from MicroChem Corp. (Newtown, MA); DMEM/F-12 medium for cell culture was bought from GIBCO (U.S.A), and Trypsin (no. 0458) and L-glutamine were purchased from Amresco (U.S.A). Both laminin and antibodies against laminin were purchased from Sigma (St. Louis, MO). Recombinant Human Ephrin-A5-Fc Chimera and Goat antiHuman Ephrin-A5 antibodies were purchased from the R&D Systems (U.S.A), and mouse against Tau-1 monoclonal antibodies were purchased from the Millipore (U.S.A). All the secondary antibodies were supplied from Boster Company. 3′,6′-Di(O-acetyl)-4′,5′-bis[N,N-bis(carboxymethyl)-aminomethyl] fluorescein, tetraacetoxymethylester (calcein-AM), and propidium iodide (PI) for cell staining were purchased from Dojindo laboratory (U.S.A.) and Sigma (St. Louis, MO), respectively. Fabrication of the Microfluidic Device. All the microfluidic devices were designed in AutoCAD software and fabricated using a two-layer soft lithography fabrication technology.34,35 The microfluidic device consists of three main channels and a number of thin interconnecting grooves, and the dimensions of the channels have been shown in Table 11650

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ator.25,26 In our previous study, we have showed that molecular gradients with gradually changed steepness could be generated by altering the velocity ratio (≠1:1) of the two fluids on a single gradient generator.9 Here, we developed a chip to demonstrate that the gradient steepness is highly tunable when the velocities of the two fluids are gradually changed while the velocity ratio is kept constant. This microfluidic device consists of three main channels (two peripheral channels and a central channel) and a number of thin interconnecting grooves (Figure 1A, and the

Immunofluorescence Staining of Substrate-Bound Molecular Gradient. At first, microfluidic channels established with substrate-bound molecular gradients were rinsed with PBS. Second, rabbit antilaminin antibodies (1:100, Sigma) or goat antihuman ephrin-A5 antibodies (20 μg/mL, R&D Systems) were perfused into the microchannels for 5 h at room temperature. Next, the microchannels were washed three times with PBS to remove surplus primary antibodies and incubated with secondary antibodies labeled with FITC (1:50) for 1.5 h at room temperature. After that, the microchannels were washed with PBS before observation. Hippocampal Neurons Culture. A suspension of dissociated primary hippocampal neurons was prepared according to the protocol previously described (neuron culture).37 Briefly, hippocampus was dissected from brain of SD rat embryonic day (E)18 embryos, followed by digestion with 0.125% trypsin for 10 min at 37 °C, and then added to the culture medium with serum to terminate the action of the trypsinase. Hippocampal neurons with the desired density (ca. 1 × 106 cells/mL) were planted into the central channels of PDMS chips, and next, the chips were placed in an incubator for 20 min allowing the cells to attach on the substrate. The attached neurons were maintained in primary culture medium of DMEM/F-12 (GIBCO) supplemented with 10% horse serum (Invitrogen), 2% B27 (GIBCO), 100 U/mL penicillin, streptomycin, and 3% L-glutamine. A low concentration of nerve growth factor (10 ng/mL) was added to the medium for neurons survival. Finally, the microfluidic chips were placed in an incubator at 37 °C, 5% CO2 for cell culture. Simultaneous Immunofluorescence Staining of Neurons and Substrate-Bound Molecular Gradient. The following sequential immunofluorescence staining procedures17,38 for neurons and substrate-bound gradient were carried out. (i) The microchannels were fixed in 4% (wt/vol) paraformaldehyde for 30 min at room temperature. (ii) The microchannels were washed three times with PBS and then permeabilized with 0.2% Triton X-100 for 15 min at room temperature. (iii) The microchannels were blocked in 10% (wt/vol) BSA for 60 min at 37 °C. (iv) Primary antibodies against substrate molecule and TAU-1 (1:1000, Millipore, MAB3420) in 3% BSA in PBS were incubated on microchannels overnight at 4 °C. (v) Secondary antibodies labeled with FITC and TRITC (1:50, Boster Company, China) were incubated for 1.5 h at 37 °C after washing the microchannels three times with PBS. (vi) Microchannels were washed three times with PBS prior to taking fluorescent images. Imaging and Data Analysis. Phase contrast and immunofluorescence staining images of substrate-bound molecular gradients and hippocampal neurons were captured using an inverted fluorescence microscope (AxioObserver Z1 fluorescent microscope with camera and incubation system, ZEISS, Germany). Normalized fluorescence intensity profiles of molecular gradients in central channels were analyzed using ImageJ (MacBiophotonics) software. An ImageJ plug-in named Neuron J was used to trace and quantify the length of the axons extending. SPSS 16.0 (SPSS Inc.) was used to perform statistical data analysis.

Figure 1. Microfluidic device for generating multiple gradients on a single chip. (A) Schematic illustration of the microfluidic device. ∗ represents the thin interconnecting grooves, and ∗∗ and ∗∗∗ represent the inlets and outlets of the main channels, respectively. (B) Simulated distribution of fluid velocity along the central channel. Red arrows represent the directions of fluid flow; a, b, and c represent the three types of chips with different dimensions for the interconnecting grooves respectively, a: C1; b: C3; c: C5. (C) Distribution curves of the simulated fluid velocity along the central channel from the inlets to the outlet for five types of chips. (D) Representative simulation of the molecular concentration gradients for three types of chips; a, b, and c represent the same types of chips as those shown in (B). The central channel (20 mm length, from the last interconnecting groove to the first one closest to the inlets) was averagely divided into 10 parts, from part I to part X, for measurement.

dimensions of the different chips are described in Table 1). When two different kinds of fluids were perfused into the central channel through two inlets, the fluid velocities gradually decreased along the central channel from the inlets to the outlet because of the bypass flow to the peripheral channels through the interconnecting grooves (Figure 1B). Consequently, molecular gradients with gradually decreased steepness were generated as the fluid velocity decreased along the central channel (Supporting Information, Figure S1). A series of theoretical calculations demonstrated that the distribution of the fluid velocity along the central channel could be effectively regulated by altering the dimensions of the thin interconnecting grooves (Figure 1C), thereby enabling the generation of a molecular concentration gradient with different distributions (Figure 1D).

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RESULTS AND DISCUSSION Mass Transport and Gradient Formation on a Laminar Flow-Based Microfluidic Device. Previous studies have demonstrated that molecular gradient steepness is correlated with the fluid velocity in a laminar-based gradient gener11651

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flow rate at the inlets were altered under three conditions (5, 10, and 20 μL/h). These results show that the distribution range of gradients would be narrowed as the flow rate increased from 5 to 20 μL/h (Supporting Information, Figure S3). In addition, we could regulate the gradient distribution by setting different flow rate ratios between the two inlets or designing the two sides of interconnecting grooves with different dimensions. Taken together, the data indicate that molecular gradients with a widely varying range of gradient steepness could be easily generated by varying several parameters such as the dimensions of the interconnecting grooves, flow rates at the inlets, and the flow rate ratio. Previously reported gradient generators could change gradient steepness by altering the control conditions25−33 (e.g., flow rate, driving pressure, molecular concentration at the inlets, and the physical shape of the device, respectively) but on different chips. Using a number of chips with different control conditions in a test may bring more experimental errors and expend more expensive biochemical reagents. Compared to these devices, the microfluidic architecture format we present here provides a facile approach to simultaneously generate gradients of uniformly varying steepness with a higher resolution on a single chip, and the steepness can be tuned in a simple and flexible way, thereby enabling precise quantification of axon response to molecular gradient steepness. Generation of Substrate-Bound Laminin Gradients. On the basis of the results of our above fluorescence characterization results, we used two types of gradient generators (C3, C4) to quantitatively analyze the substratebound laminin (a component of extracellular matrix, Mw ≈ 900 kDa) gradients with varying steepness. To ensure the successful transfer of fluidic molecular gradient to substrate-bound gradient, we simulated the surface concentration of the adsorbed proteins by taking protein adsorption kinetics into the calculation (the simulation process was described in detail in the Supporting Information). The plot of fluorescence intensity versus surface-bound density of protein within the middle channel was obtained according to the plot of fluorescence intensity versus the FITC-conjugated IgG density (Supporting Information, Figure S4). The results demonstrated that the simulated gradient profile fit well with the experimental data (Supporting Information, Figure S5), and the surface density of proteins remained stable after being adsorbed for 8 h (Supporting Information, Figure S6). The representative fluorescence intensity profiles and images of substrate-bound laminin gradients generated on the two types of chip are presented Figure 3A,B, respectively. On chip C3, the substrate-bound laminin gradients were mainly generated on the right half (450−900 μm) region of the central channel (Figure 3Aa) because of the lower diffusion coefficient in comparison with FITC-labeled dextran (Mw = 70 kDa). We analyzed the gradient steepness from part I to part VIII (approximately linear gradients in each part) for the right half to quantify the gradient distributions of the two gradient generators (Figure 3C). The distribution of gradient steepness ranged from 0.17% (part I) to 1.49% (part VIII) on chip C3 and from 0.02% (part I) to 0.61% (part VIII) on chip C4. These values clearly indicate that chip C3 could generate substrate-bound laminin gradients with more widely but evenly distributed steepness and that the difference in gradient steepness between two adjacent parts could be less than 0.1% (resolution 6.5 times) on parts IV and VIII, while only little change ( 1% (Figure 4E) and were significantly different from negatively extended axons when s ≈ 1.5%. Generation of Substrate-Bound Ephrin-A5 Gradients and Statistical Analysis of Axonal Response. Ephrin-A5 (Mw = 48.6 kDa) is a ligand that interacts with the transmembrane receptor ephrin (Eph) family of the tyrosine kinases.3,45 Increasing evidence indicates that ephrin-A5 that is locally expressed within a gradient could guide the formation of hippocampal topographic maps through repulsive actions;11,46 however, the regulated functions of ephrin-A5 are imprecise because of the intricate expression pattern in time and space in vivo.12,47 Quantifying the biased response to substrate-bound ephrin-A5 gradients with different steepness levels in the initial outgrowth of hippocampal axons could help in accurately mapping the in vivo expression patterns and correctly controlling the axonal growth trajectory in relevant studies. Considering previous characterizations, we selected chip C3 to generate substrate-bound ephrin-A5 molecule gradients with

Figure 5. Generation of ephrin-A5 gradients and analysis of axonal responses. (A) Normalized fluorescence intensity profile of substratebound ephrin-A5 gradients generated on C3 chip; the colored curves represent different parts of gradient generation. (B) The profile showing the distribution of ephrin-A5 gradient steepness on C3 chip. Error bars are SEM, n = 5. (C) A representative immunofluorescence micrograph of hippocampal neurons growing down the substratebound ephrin-A5 gradient; hippocampal neurons were stained with anti-Tau-1 after 24 h in culture. The yellow arrow represents the direction of the ephrin-A5 gradient; the white arrows represent the neurons growing down the ephrin-A5 gradient. Scale bar = 100 μm. (D) The guidance ratios of neurons response to ephrin-A5 gradients with varying steepness on the nine parts (from part I to part VIII; C represents the control group) after culture for 24 h. (one-way ANOVA; ***p < 0.001; **p < 0.01; n.s., not significant). Error bars are SEM, n = 3 (the number of neurons on each part is greater than 350). (E) The histogram showing the fold increase [FI, FI = (Grx − Grc)/Grc] of the axonal guidance ratio on different parts (x represents the parts from part I to VIII; c represents the control group) compared with the control experiment. The blue curve represents the FI differences (FIx − FIx−1) between the adjacent parts, and the red arrow represents a significant increase on part III. (F) Statistical analysis of the neuritis number of differentiated neurons on different parts of the central channel on the C3 chip after culture for 24 h. The red and black curves indicate the percentage of neurons with more than two (N ≥ 2) and three (N ≥ 3) neurites on different parts. Error bars are SEM; the statistical number of hippocampal neurons were 347 (VII− VIII), 449 (V−VI), 820 (III−IV), and 562 (I−II), respectively.

with the simulated results (Supporting Information, Figure S10). Obviously, the ephrin-A5 gradients were mainly generated on the left half region (0−450 μm) of the central channel because of to its higher diffusion coefficient; thus, we quantitatively analyzed the gradient steepness of substratebound ephrin-A5 from part I to part VIII on the left half (approximately linear gradients in each part) of the central channel (Figure 5B). We observed that the range of the 11654

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data show that both substrate-bound laminin and ephrin-A5 gradients could effectively initiate the biased differentiation of hippocampal neurons. The absolute value of axonal guidance ratios gradually increased as the gradient steepness increased. Hippocampal neuronal guidance ratios showed a significant increase when the steepness of laminin and ephrin-A5 gradients were greater than 0.5% and 0.1%, respectively. Furthermore, the axons could respond with high sensitivity to very shallow laminin and ephrin-A5 gradients. The lengths of positively extended axons increased as the laminin gradient steepness increased, whereas the ephrin-A5 gradient had no significant effect on the axonal lengths within the steepness range investigated in this study. As a repulsive factor, the increased concentration of ephrin-A5 decreases the number of neurites in hippocampal neurons during the initial outgrowth. Our findings provide further detailed information on how and to what extent different steepnesses of substrate-bound laminin and ephrin-A5 gradients guide hippocampal neuron development during the initial outgrowth. The present findings enhance our understanding of the axonal response mechanism to substrate-bound laminin and ephrin-A5 gradients as well as accurate mapping of the in vivo expression patterns of these two molecules. In addition, the present findings provide a strong basis for controlling axonal growth trajectories to help restore neuronal connectivity after injury in addition to degradation using guidance factors. This study manifests the capability of our gradient generator to create molecular gradients with a highly tunable steepness and obtain detailed information on two substrate-bound molecular gradients that direct axon specification. In the future, our device will be adapted to gain deeper insights into the mechanisms of responses to molecular gradients for neurons and other types of cells.

gradient steepness was from 0.02% (part I) to 1.31% (part VIII). After generating substrate-bound ephrin-A5 gradients on chip C3, hippocampal neurons were seeded and cultured in the central channel, as described previously. Representative immunofluorescence and phase contrast images of hippocampal neurons (cell bodies were in the left half region) after being cultured for 24 h on an ephrin-A5 gradient substrate are shown in Figures 5C (acquired from part VI) and S11, Supporting Information, respectively. These images show that specialized axons grew down the ephrin-A5 gradient because of its repulsive actions. The classification of the positive and negative axonal responses to the molecular gradient were the same as those described above (Figure 4B). The data indicated that the axonal response to the ephrin-A5 gradient was negative and that the absolute value of guidance ratios on the eight parts (from part I to part VIII) gradually increased as the gradient steepness increased (Figure 5D). Compared with the control group, the axonal guidance ratios on part I (s = 0.02%) and part II (s = 0.03%) showed few differences [one-way analysis of variance (ANOVA); n.s., not significant], whereas significant increases were observed from parts III (s = 0.10%) to VIII (s = 1.31%) [one-way analysis of variance (ANOVA), **p < 0.01, ***p < 0.001]. Analysis of FI of guidance ratio indicated that the minimal FI is approximately 2.5 times on part I, whereas the maximal FI is approximately 21 times on the part VIII (Figure 5E). Further analysis on FI differences between adjacent parts revealed a significant increase (>5 times) on part III (Figure 5E). We measured the length of axons cultured for 24 h to investigate whether their growth rates varied when the ephrinA5 gradient steepness varied. There was no statistical difference in axonal length between positively and negatively extending axons for all eight parts (Supporting Information, Figure S12, one-way ANOVA; n.s., not significant). To further test the direction of local ephrin-A5 during neuronal development, we examined the neuritic number on different parts for every differentiated neuron. We observed that the percentage of neurons with more than two or three neurites decreased as the average concentration of ephrin-A5 increased (Figure 5F). Taken together, ephrin-A5 showed a significant repulsive effect on hippocampal neurons during their initial outgrowth when the gradient steepness was greater than 0.1%. The absolute value of the axonal guidance ratio also gradually increased as the substrate-bound ephrin-A5 gradient steepness increased in the range investigated in this work. Compared with the control group, the absolute value of axonal guidance ratios significantly increased even when the steepness of ephrin-A5 gradients was as low as 0.1%, indicating that hippocampal neurons could respond to an ephrin-A5 gradient with extremely low steepness. In addition, the statistical results of axonal length and neuritic number indicate that the local ephrin-A5 concentration plays an important role, along with the gradient steepness, in directing neuronal development.

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ASSOCIATED CONTENT

S Supporting Information *

Detailed procedures of theoretical simulation and Figures S1− S12. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (86)2768752149. Fax: (86)2768754067. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Basic Research Program of China (973 Program, No. 2012CB720603), National Science Foundation of China (Nos. 21375099, 31070995), Specialized Research Fund for the Doctoral Program of Higher Education (20120141110031), and the Fundamental Research Funds for the Central Universities (2042014kf0192).

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CONCLUSIONS We present a versatile and robust quantitative device with a novel microfluidic architecture format capable of generating molecular gradients with evenly varying steepness to quantify the biased axonal response to substrate-bound laminin and ephrin-A5 gradients. The overall range and resolution of the gradient steepness could be precisely and flexibly controlled by adjusting various parameters of the device. Our experimental

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dx.doi.org/10.1021/ac504159g | Anal. Chem. 2014, 86, 11649−11656