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First published online 21 September 2005
doi: 10.1242/dev.02029

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Adaptation is not required to explain the long-term response of axons to molecular gradients

¹ Department of Neuroscience, Georgetown University Medical Center, 3900 Reservoir Road NW, Washington, DC 20007, USA
² Department of Physics, Georgetown University, 37th and O Streets NW, Washington, DC 20057, USA
³ Queensland Brain Institute, Department of Mathematics and Institute for Molecular Bioscience, University of Queensland, St Lucia, QLD 4072, Australia

View larger version (67K): [in a new window]   Fig. 1. Typical dorsal root ganglia (DRG) explants generated experimentally by Rosoff et al. (Rosoff et al., 2004) (A,B), and by the computational model (C,D). In A,C, there is no nerve growth factor (NGF) gradient; in B,D, an exponential NGF gradient is present increasing upwards in the figure with a fractional change of 0.2% over 10 µm. All images are 480x480 pixels and presented at the same scale. The diameter of the explants in the simulated cases is 700 µm.

View larger version (10K): [in a new window]   Fig. 2. Sensitivity of the model (as measured by the guidance ratio) to its parameters. (A) Proportion of neurites competent to respond to the gradient. Response increases roughly linearly with this proportion. (B) Width of spatial averaging, i.e. effective spatial spread of signaling effects downstream from receptor binding. Note the peak at 5%. (C) Duration of temporal averaging, i.e. the time over which signaling effects decay.

View larger version (16K): [in a new window]   Fig. 3. Match of the model results to the experimental data of Rosoff et al. (Rosoff et al., 2004). Parameters used are shown in Table 1, with KD=3 nM. (A) Response as a function of gradient steepness for an absolute concentration of 1 nM. (B) Response as a function of absolute concentration for a gradient steepness of 0.2%. The solid red curves show the data originally plotted by Rosoff et al. (Rosoff et al., 2004), whereas the dashed red curves show the revised experimental data that is obtained if all of the explants from the 0.2% gradient/1 nM condition are averaged together (see text).

View larger version (25K): [in a new window]   Fig. 4. The complete two-dimensional sensitivity surface for the model. Note that the peak along the concentration axis becomes higher and broader at the higher values of gradient steepness.