Figure 1.
Schematic of growth cone interaction with nano-PPX surfaces.
(a) SEM image of typical nano-PPX substrate indicating the 0 and π radians directions with respect to nanorod tilt. (b) Schematic defining the measurement of growth angle θ with respect to the 0 and π directions. The schematics also show the deterministic torques γo and γπ and the corresponding direction of axonal rotation imparted by these torques. The two angular domains used for data analysis are: −π/2 ≤ θ ≤ + π/2 and π/2 ≤ θ ≤ 3π/2. For the purpose of the analysis −π/2 is identified with 3π/2 (Figures 3–6 below). (c) Schematics of growth cone turning in response to asymmetric torques γπ and γ0 (growth model described in the main text).
Figure 2.
Examples of nano-PPX surface ratchets.
(a) Left: AFM topographical image (20×20 µm) of a nano-PPX substrate where the nanorods point in the π radians direction; Right: AFM line scan across the substrate illustrating the ratchet topography. The ratchet is oriented in the 0 radians direction (i.e. opposite to the nanorod tilt). (b) AFM topographical image (20×20 µm) and AFM line scan illustrating a nano-PPX substrate where the ratchet points in the π radians direction (i.e. the same direction as the nanorod tilt). (c) Schematics defining ratchet angles α0 and απ with respect to the 0 and π radians directions. d) Schematics illustrating the conditions: Cα = απ/α0 > 1 (i.e. nanorods tilt in the same direction as the ratchet structure) and Cα = απ/α0 < 1 (i.e. nanorods tilt in the opposite direction to the ratchet structure).
Figure 3.
Angular distributions of axonal outgrowth.
(a–c) Examples of unidirectional axonal outgrowth on nano-PPX substrates with different Cα (as defined in Fig. 2 c) and axonal angular distributions both in the nanorod tilt direction (histogram peaks at π radians) and opposite to the rod tilt direction (histogram peaks at 0 radians). Axons and cell bodies are shown in green (fluorescence images). Segment count represents the number of axon segments, each one of 20 µm in length. The fluorescent images show representative regions from samples of a given type (labeled by Cα). Axonal growth for unmodified cells was measured on a total number of n = 21 different substrates, distributed as follows: three substrates with Cα = 0.6 ± 0.2; one substrate with Cα = 1.26 ± 0.3; four substrates with Cα = 1.4 ± 0.4; three substrates with Cα = 1.8 ± 0.5, three substrates with Cα = 2.1 ± 0.3; four substrates with Cα = 2.4 ± 0.2, and three substrates with Cα = 3.0 ± 0.9. The total number of cells measured for each type of substrate was between 160–350. (a) Example of growth on nano-PPX surfaces with Cα = 2.4 ± 0.2. Left: representative fluorescence image of neuron outgrowth on this type of surfaces. Right: histograms showing the angular distributions of axonal outgrowth centered at π and 0 radians, respectively. The histograms show the mean and the standard error of the mean for n = 4 different substrates with a total of 350 axons (total measured axon outgrowth length on these surfaces is 120 mm). (b) Left: representative fluorescence image showing axonal outgrowth on a nano-PPX surface with Cα = 1.4 ± 0.4. Right: histograms showing angular distributions centered at π and 0 radians, respectively. The histograms show the mean and the standard error of the mean for n = 4 different substrates with a total of 312 axons (total measured axon outgrowth length on these surfaces is 106 mm). The maximum outgrowth in (a–b) is observed at π radians. One way ANOVA followed by pair-wise comparison using Tukey's HSD test shows statistically significant difference between outgrowth centered at π vs. 0 radians (p<0.05 for both types of surfaces, see Table S2). (c) Left: representative fluorescence image showing axonal outgrowth on a nano-PPX surface with Cα = 0.6 ± 0.2. Right: corresponding angular distributions centered at π and 0 radians, respectively. The histograms show the mean and the standard error of the mean for n = 3 different substrates with a total of 252 axons (total measured axon outgrowth length on these surfaces is 81 mm). The maximum outgrowth in (c) is observed at 0 radians (one way ANOVA followed by pair-wise comparison using Tukey's HSD test indicates statistical significance with p<0.05, see table S2). For all angular distributions the maximum outgrowth is always observed in the ratchet direction (π radians for Cα>1 and 0 radians for Cα<1). The statistical significance for all types of surfaces is shown by the one-way ANOVA followed by pair-wise comparison using Tukey's HSD test in Table S2 (comparison between pairs of peaks centered at π vs. 0 radians, for a given surface type) and Table S3 (comparison between distributions for different values of Cα).
Figure 4.
Examples of normalized experimental angular distributions for axonal growth.
Normalized experimental angular distributions for axonal growth and fits with Eq. 3 (red curves) for two types of surfaces displaying opposite ratchet asymmetries. (a) Normalized angular distribution and fit with Eq. 3 (red curve) for axonal growth in the region π/2 ≤ θ ≤ 3π/2, on all substrates with Cα = 3.0 ± 0.9 (i.e. maximum asymmetry in the nanorod direction). (b) Normalized angular distribution and fit with Eq. 3 (red curve) for axonal growth in the region −π/2 ≤ θ ≤ +π/2 on the same type of surfaces as in (a). (c) Normalized angular distribution and fit with Eq. 3 (red curve) for axonal growth in the region π/2 ≤ θ ≤ 3π/2, on all substrates with Cα = 0.6 ± 0.2 (asymmetric ratchet pointing opposite to the rod tilt direction). (d) Normalized angular distribution and fit with Eq. 3 (red curve) for axonal growth in the region −π/2 ≤ θ ≤ +π/2 on the same type of surfaces as in (c). The inset in each figure shows the ratio between the corresponding asymmetric torque (γπ or γo) and the angular diffusion coefficient Dθ. This ratio is obtained from fitting the experimental data with Eq. 3. The total measured axon outgrowth length for (a–b) is 75 mm (for a total of 241 axons). The total measured axon outgrowth length for (c–d) is 78 mm (for a total of 273 axons).
Figure 5.
Cell-surface coupling versus ratchet asymmetry.
Variation in the strength of the cell-surface coupling asymmetry γπ/γ0 with increasing ratchet asymmetry Cα for all 7 types of surfaces measured in the current study. Error bars for the ratchet angle ratios Cα represent experimental uncertainties obtained from the standard deviations of measured ratchet angles via AFM. Error bars for the coupling asymmetry γπ/γ0 represent uncertainties obtained from the fit of the normalized angular distributions with Eq. 3.
Figure 6.
Axon outgrowth for drug-treated neurons on nano-ppx.
Examples of axon outgrowth (left) and angular distributions for axonal outgrowth (right) on nano-PPX surfaces with Cα = 2.4 ± 0.2 for neurons cultured with 10 nM Taxol (a) or 10 µM Blebbistatin (b). The histograms show the mean and the standard error of the mean for n = 4 different substrates for each drug. The total measured axon outgrowth length is 68 mm for (a) (total of 285 axons) and 91 mm for (b) (total of 327 axons). The peaks of the angular distributions at 0 and π radians for both (a) and (b) are clearly reduced compared to the non-treated cells (Fig. 3), indicating a drastic decrease in surface-induced directional growth for drug (Taxol or Blebbisttain) treated cells. One way ANOVA shows no statistically significant difference between outgrowth centered at π vs. 0 radians for the drug treated cells (p>0.1, Table S2), demonstrating that there is no unidirectional bias in this case. The ratio between the corresponding asymmetric torque (γπ or γo) and the angular diffusion coefficient Dθ obtained from fitting the experimental data with Eq. 3. is shown in Table S1 and Fig. S5–S7.