Fig 1.
NGF dependence of neurite growth and fasciculation.
DRG explants and dissociated cells grown in collagen for 48 h with various NGF concentrations were stained with TuJ1 for neurite visualisation. (A,B) Representative examples of explants at 0.3 nM and 10 nM demonstrate the reduction in outgrowth at high NGF concentrations (scale bars 500 μm). (C) Quantification of average explant outgrowth shows a biphasic NGF dependance. Red markers correspond to individual explants, error bars are SEM. (D,E) Representative examples of dissociated cells at 0.3 nM and 10 nM demonstrate the absence of growth inhibition (scale bars 100 μm). (F) Quantification of dissociated-cell neurite lengths. Black lines are medians, black squares are means, and red crosses are outliers from 20 − 156 cells per condition. (G,H) Representative images of neurites extending from explants in 0.3 nM and 10 nM NGF concentrations at higher magnification (scale bars 50 μm). (I) A comparison of neurite bundle widths shows no increase in fasciculation at 10 nM NGF. Our method of image analysis easily detects differences in control sample patches of thin and thick bundles.
Fig 2.
Analysis of NGF gradient data set.
(A) Example image from the data set of ref. [18], which documents the total growth of DRG explants after 48 h in shallow NGF gradients. Experimental conditions were varied over gradient steepnesses 0 − 0.3% concentration change per 10 μm, and background concentrations of ≈ 0.001 − 100 nM (scale bar 500 μm). (B) Average radial outgrowth, quantified by Fourier coefficient a0, has a biphasic dependence on background NGF concentration, and is largely independent of gradient steepness. (C) Directional bias up the gradient, quantified by normalised coefficient b1/a0, was observed over background concentrations 0.01 − 1 nM, implying a high sensitivity to NGF.
Fig 3.
Signalling networks for neurite growth and gradient sensing.
Activating (A) and inhibitory (I) signalling pathways are stimulated in parallel by NGF at the growth cone c1, and within the ganglion c2. By sensing an asymmetry in concentrations between growth cone and cell body, an extracellular gradient can be detected. (A) Model 1: growth. The signals are integrated by conversion of a substrate G to a growth promoting active form G*. (B) The steady-state output of the growth model, (, black line, normalised by maximum value) reproduces the biphasic ganglion outgrowth response in uniform concentrations (c1 = c2), and saturating dissociated cell response (c2 = 0, dotted line). Black squares are data replotted from Fig 1C, normalised by the maximum outgrowth at 0.3 nM. Due to these two constraints, the network lacks the sensitivity for gradient detection. The model response with a 50% asymmetry in inputs (c1 = 1.5c2, c2 defined by the x-axis; red line) shows only a small increase over the uniform condition. Parameters: k0 = 1, k1 = 100, k2 = 0.75 and KI = 5 nM. (C) Model 2: gradient detection. Signal integration occurs through intermediaries X and Y that convert a protein F to an active form F*. Dual negative regulation from an interaction between A and I yields a sensitive readout of the ratio c1/c2 in the steady-state output. (D) Gradient detection is robust to parameter perturbations for concentrations of 0.001 − 1 nM. For each pair (c1, c2), the average response over 100 trials with noisy parameters is shown. An output of
indicates the ‘decision’ that c1 = c2,
indicates c1 > c2, and
indicates c1 < c2. Parameters as described in Methods.
Fig 4.
Coupled growth and gradient detection.
The motifs depicted in Fig 3A and 3C are coupled together in a two-compartment model of a neurite. Activated receptors A are retrogradely transported from the growth cone to cell body to form a population Ac, and the inhibitory signal I is anterogradely transported to the growth cone to form a copy Ig. The output of the cell-body compartment F* regulates the supply of the substrate G at the growth cone.
Table 1.
Model parameters for coupled growth and gradient detection.
Fig 5.
Model simulations and predictions.
(A,B) Simulations of the model yield good agreement with experimental data, reproducing both the biphasic average radial outgrowth (A) and sensitive gradient response (B). Coloured markers are data replotted from Fig 2, error bars are SEM. (C) Predicted relief of growth inhibition when distal neurites are exposed to high NGF concentrations while the ganglion body is held at 1 nM. The full model exhibits a switch-like response as the distal neurite concentration exceeds that of the ganglion body (dashed line). Without the gradient sensor, the model response is less steep (dotted line). The biphasic curve from (A) is replotted for comparison (solid line). (D) Predicted temporal response to a 500 min pulse of NGF. A transient global doubling of NGF concentration (red line) produces a large out of phase change in growth rate (solid black line) due to time delays from transport. Increasing the rates of transport suppresses this effect (dashed black line). Parameters used in the simulations are given in Table 1.