Fig 1.
Examples of cultured cortical neurons on PDL coated PDMS surfaces with periodic micro-patterns.
(a) Neurons imaged at t = 6 hrs after plating. (b) Neurons imaged at t = 24 hrs after plating. (c) Neurons imaged at t = 48 hrs after plating. (d) Neurons imaged at t = 72 hrs after plating. The main structural components of a neuronal cell are labeled in (a). The scale bar shown in (a) is the same for all images. The angular coordinate θ used in this paper is defined in the inset of Fig 1A. All angles are measured with respect to the x axis, defined as the axis perpendicular to the direction of the PDMS patterns (see Fig 2).
Fig 2.
Image of a PDMS surface and definition of the coordinate system.
(a) Topographic Atomic Force Microscope (AFM) image of a PDL coated PDMS patterned surface (top), and example of an AFM line scans obtained across the surface (bottom). (b) Coordinate system and the definition of the angular coordinate θ used in this paper. The x axis is defined as the axis perpendicular to the direction of the PDMS patterns. The directions corresponding to θ = 0, π/2, π, and 3π/2, and the pattern spatial period d (defined as the distance between two neighboring ridges) are also shown in (a). The line scan in (a) demonstrates that the patterns are periodic in the x direction, and have a constant depth of approximately 0.5 μm. The pattern spatial period is d = 3 μm.
Fig 3.
Examples of normalized speed distributions for growth cones measured on PDMS substrates.
(a) Speed distribution for N = 168 different growth cones, measured at t = 6 hrs after plating. The continuous red curve represents fit with the Gaussian distribution given by Eq 6. (b) Speed distribution for N = 189 different growth cones measured at t = 24 hrs after plating. The continuous red curve represent fit with the Gaussian distribution given by Eq 6. (c) Speed distribution for N = 176 growth different cones measured at t = 48 hrs after plating. (d) Speed distribution for N = 192 different growth cones measured at t = 72 hrs after plating.
Fig 4.
Variation of the velocity autocorrelation function and axonal mean square length with time.
(a) Data points: experimentally measured velocity autocorrelation function vs. time. The continuous red curve represents the fit of the data points measured for t < 48 hrs with the prediction of the theoretical model based on the Ornstein-Uhlenbeck process (Eq 7). (b) log-log plot of axonal mean square length vs. time. The continuous red curve represents the fit to the data measured at t < 48 hrs with Eq 8 (prediction of the theoretical model based on the Ornstein-Uhlenbeck process). The dotted blue curve represents the fit to the data points measured for t ≥ 48 hrs with a power-law function (Eq 11 and Eq 15). Each data point in (a) and (b) was obtained by measuring between N = 150 and N = 195 different axons (corresponding to 5–10 different fluorescent images per time data point). Error bars in both figures indicate the standard error of the mean. The fit of the data in with Eq 7 for (a), and Eq 8 for (b) give the diffusion coefficient D and the constant damping coefficient γ of the Ornstein-Uhlenbeck process (see text).
Fig 5.
Examples of normalized experimental angular distributions for axonal growth.
The vertical axis (labeled Normalized Frequency) represents the ratio between the number of axonal segments growing in a given direction and the total number N of axon segments measured at a given time t. Each axonal segment is of 20 μm in length (see Data Analysis section). (a) Data for N = 1724 different axon segments obtained at t = 6 hrs after plating. (b) Data for N = 2078 different axon segments obtained at t = 24 hrs after plating. (c) Data for N = 2405 different axon segments obtained at t = 48 hrs after plating. (d) Data for N = 2629 different axon segments obtained at t = 72 hrs after plating. The data shows that the axons display strong directional alignment along the surface patterns (peaks at θ = π/2 and θ = 3π/2), with the degree of alignment (sharpness of the distribution) increasing with time. The continuous red curves in each figure represent fit to the data points using Eq 14. The fit gives the ratio γθ/Dθ between the deterministic torque and the diffusion coefficient for the angular motion, at each time point (see text).
Fig 6.
Variation in time of the ratio between the deterministic torque and the diffusion coefficient for the angular motion.
The increase in the ratio γθ/Dθ reflects the increase in the cell-surface interactions as discussed in the text. Error bars indicate the uncertainties obtained from the fit of the normalized angular distributions (Fig 5).