An important mechanism during nervous system development is the guidance of axons by chemical gradients. The structure responsible for responding to chemical cues in the embryonic environment is the axonal growth cone -- a structure combining sensory and motor functions to direct axon growth. In this thesis, we develop a series of mathematical models for the gradient-based guidance of axonal growth cones, based on the idea that growth cones might be optimised for such a task. In particular, we study axon guidance from the framework of Bayesian decision theory, an approach that has recently proved to be very successful in understanding higher level sensory processing problems. We build our models in complexity, beginning with a one-dimensional array of chemoreceptors simply trying to decide whether an external gradient points to the right or the left. Even with this highly simplified model, we can obtain a good fit of theory to experiment. Furthermore, we find that the information a growth cone can obtain about the locations of its receptors has a strong influence on the functional dependence of gradient sensing performance on average concentration. We find that the shape of the sensitivity curve is robust to changes in the precise inference strategy used to determine gradient detection, and depends only on the information the growth cone can obtain about the locations of its receptors. We then consider the optimal distribution of guidance cues for guidance over long range, and find that the same upper limit on guidance distance is reached regardless of whether only bound, or only unbound receptors signal. We also discuss how information from multiple cues ought to be combined for optimal guidance. In chapters 5 and 6, we extend our model to two-dimensions, and to explicitly include temporal dynamics. The two-dimensional case yields results which are essentially equivalent to the one dimensional model. In contrast, explicitly including temporal dynamics in our leads to some significant departures from the one-dimensional and two-dimensional models, depending on the timescales over which various processes operate. Overall, we suggest that decision theory, in addition to providing a useful normative approach to studying growth cone chemotaxis, might provide a framework for understanding some of the biochemical pathways involved in growth cone chemotaxis, and in the chemotaxis of other eukaryotic cells.
| Identifer | oai:union.ndltd.org:ADTP/254234 |
| Creators | Duncan Mortimer |
| Source Sets | Australiasian Digital Theses Program |
| Detected Language | English |
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