Modeling axon outgrowth in an inhomogeneous environment
Pieter Laurens Baljon (VU University Amsterdam), Jaap van Pelt (VU University Amsterdam), Arjen van Ooyen (VU University Amsterdam)
- Growth cones' sensitivity to their environment allows for anisotropic outgrowth and targeted innervation of brain structures such as layers.
- The added complexity of parameters in the growth model and their interactions necessitated a new parameter estimation procedure based on the likelihood of parameters. The validation of the model-generated neuronal structures requires optimization of growth parameters and statistical comparison with experimental data.
The parameter estimation procedure also provides a way to formally compare two classes of morphologies based on the likelihood of their parameters, rather than on the statistics (shape properties) themselves. Intuitively a test in statistics space is more arbitrary, as there is a lot of freedom in the choice of statistics. By contrast, a comparison by confidence intervals for growth parameters incorporates the sensitivity of morphological statistics to those parameters. Furthermore, it allows to hypothesize the role of developmental mechanisms through the parameters using standard multivariate techniques.
We found a marked similarity between parameters for different types of dendrites. The difference between axons and dendrites by contrast centers on only a subset of parameters which allows for hypothesizing on underlying mechanisms that can be tested in biophysical models (for instance in CX3D, Zubler et al.). In addition, we demonstrate a validation of this estimation procedure using synthetic data: maximum likelihood parameters are estimated to mimic morphologies that were themselves generated by NETMORPH with known parameters.