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. 2012 Nov 6;24(2):487–500. doi: 10.1093/cercor/bhs327

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© The Author 2012. Published by Oxford University Press.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/3.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com.

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Figure 9. — (A) Development of axonal long-range projections on a single-patch system. Growth cones of randomly selected cells follow the gradient of an extracellular cue secreted by cells located inside the patches. This same cue promotes more dense arborization by increasing the probability of the axon to bifurcate. (1) Initially, cells extend their axons in random directions. The yellowish somata are the strongest producers of the guidance cue. Newly extended axons and their cell bodies are colored red. (2 and 3) The region of high guidance cue concentration (yellow cell bodies) already has denser arborizations. (4) Arborization pattern at progressed stage. For the sake of clearer visualization, we set the bifurcation probability outside the patches to be quite low. (B) Sequence of axonal growth on multiple patch systems from the pattern in Figure 6B. This axonal growth rule makes use of many patchy patterns generated by the Gierer–Meinhardt model. In contrast to the simpler growth rule with only 1 global patch system, in this case, the location of the soma determines the targeted activator type (different colors indicate different types). Axons that arise from cell bodies lying in a patch will make long-range projections only to the patches of a similar identity. Cell bodies that are not located inside a region of high activator and inhibitor concentration levels make only nonspecific local connections. The specificity of the resulting connections can be controlled by the parameters of the growth model. For example, as mentioned in the Materials and Methods section, the probability to bifurcate is given by , where is the concentration of the activator substance and u, v are variable parameters. Large v increases the probability to branch outside of the patches, leading to less specific connectivity. In the scenario with multiple patch systems, a growth cone could also target activator patches of multiple types with different scaling parameters u, such that the communication between different patch systems is increased. Additionally, the bifurcation could be guided by the inhibitor substance, which increases the overlap between different patch systems (as shown in Fig. 6B,C).

Inline graphic — (A) Development of axonal long-range projections on a single-patch system. Growth cones of randomly selected cells follow the gradient of an extracellular cue secreted by cells located inside the patches. This same cue promotes more dense arborization by increasing the probability of the axon to bifurcate. (1) Initially, cells extend their axons in random directions. The yellowish somata are the strongest producers of the guidance cue. Newly extended axons and their cell bodies are colored red. (2 and 3) The region of high guidance cue concentration (yellow cell bodies) already has denser arborizations. (4) Arborization pattern at progressed stage. For the sake of clearer visualization, we set the bifurcation probability outside the patches to be quite low. (B) Sequence of axonal growth on multiple patch systems from the pattern in Figure 6B. This axonal growth rule makes use of many patchy patterns generated by the Gierer–Meinhardt model. In contrast to the simpler growth rule with only 1 global patch system, in this case, the location of the soma determines the targeted activator type (different colors indicate different types). Axons that arise from cell bodies lying in a patch will make long-range projections only to the patches of a similar identity. Cell bodies that are not located inside a region of high activator and inhibitor concentration levels make only nonspecific local connections. The specificity of the resulting connections can be controlled by the parameters of the growth model. For example, as mentioned in the Materials and Methods section, the probability to bifurcate is given by , where is the concentration of the activator substance and u, v are variable parameters. Large v increases the probability to branch outside of the patches, leading to less specific connectivity. In the scenario with multiple patch systems, a growth cone could also target activator patches of multiple types with different scaling parameters u, such that the communication between different patch systems is increased. Additionally, the bifurcation could be guided by the inhibitor substance, which increases the overlap between different patch systems (as shown in Fig. 6B,C).