Brian Taba, PhD
Learning: Axon Guidance

Personal Background

I received my BS in electrical engineering from Caltech in 1999. During my time there, I became interested in computation and neural systems, a multidisciplinary approach to studying the brain that combines engineering with neurobiology in order to tease out the underlying principles that enable the brain's amazing capabilities. After graduating I came to the University of Pennsylvania to study neuromorphic engineering from the master, Dr. Kwabena Boahen.


Brian Taba

Research Goals

The ultimate goal is to make an artificial brain. The lab has had some success devising the first stage, the silicon retina, which includes thirteen different cell types, each of which had to be explicitly hardwired. Unfortunately, the human brain has something on the order of a trillion neurons, divided into a taxonomy of undetermined order, and we would rather not have to trace every circuit out by hand. We would like to derive a simple local design rule that can self-organize neural circuits automatically.

During development, the visual pathway wires axons from the retina to the thalamus and thence to visual cortex. Axons are guided to their destinations by growth cones at their ends. A growth cone is a labile amoeboid structure that extends and retracts finger-like filopodia in all directions, eventually settling on a particular direction by extending more filopodia on one side and retracting more from the other side. This navigation decision can be influenced by extracellular chemicals.

After making many biologically semi-plausible simplifying assumptions, I made a chip that implements a model of chemical-guided axon guidance. The premise is that presynaptic cells project growth cone-tipped axons to activate postsynaptic targets. Active postsynaptic cells release a diffusive guidance chemical called neurotropin into the environment, which attracts simultaneously active growth cones. The growth cones of temporally coactive presynaptic cells tend to congregate in postsynaptic space, since growth cones can cooperate to trigger neurotropin release and therefore neurotropin is maximized when all the growth cones that are active at the same time are exciting the same place.

The eventual goal is to cascade neuromorphic chips obeying this sort of plasticity rule so that the system will automatically wire itself without explicit designer specification for each point-to-point connection. An example of such a system might include two silicon retinae and one neurotropin chip, which would take the two inputs and segregate ocular dominance columns, topographic maps, and orientation selective receptive fields.

Project Status

I sent out a chip, Neurotrope1, that implements a neurotropic model of developmental plasticity. After two years of testing it finally resembles a working project. Here's an animation that sums up just about everything.

Modeling Epigenetic Development Axon-terminals from randomly-activated patches of retinal cells (top-left) excite tectal cells (top-right) to release neurotropin, a chemical that diffuses to nearby locations. Migrating up the neurotropin gradient, axons from neighboring retinal cells converge on neighboring tectal cells. Coloring retinal cells (bottom-left) and tracing the colors reveals a map forming in the tectum (bottom-right). This simulation was performed by Neurotrope1: electrons emulate neurotropin and softwires emulate axon-migration. [Brian Taba 2002]

The top row of the animation is the stimulus protocol. The retinal ganglion cell array is on the left and the target neuron array on the right. To generate input correlations I activate contiguous patches in the retinal plane centered on random cell bodies (red). This activity is transmitted through the connectivity matrix (center) to the corresponding growth cones. In a working system, the active growth cones will cluster together in the target plane the same way their cell bodies are clustered in the retinal plane. I define an error measure for a given retinal cell (red) as the average distance in the target plane between its growth cone and the growth cones of its three nearest retinal neighbors (green).

The bottom row of the animation shows the state of the topographic projection. The retinal plane (left) is topographically stained. This dye is carried from the cell body through the axon to the growth cone, creating a much sloppier color map in the target plane (right). Repeated patch presentation refines the color continuity. In a perfectly topographic projection, these maps would be identical.

Here's a little more about the project history behind Neurotrope1.

More recently, I've been trying to characterize the factors that limit growth cone guidance in this system. The figure below shows the effect of varying the neurotropin diffusion radius on supervised topographic map refinement.

Optimal neurotropin diffusion radius. Coactive immobile peers attract mobile growth cones in a simulation of isthmotectal retinotopic map refinement. A Stationary distribution of distances (r) separating a growth cone from its immobile peer for a population of growth cone pairs. A perfectly guided growth cone would be colocalized with its peer at r=0. B Average distance (±standard deviation) versus neurotropin diffusion-radius. Growth cone guidance is optimized at intermediate diffusion radii.

In this set of experiments, a fixed topographic synaptic projection supervises the topographic refinement of a dynamic growth cone population. Each mobile growth cone is paired with an immobile synapse and both axon terminals are simultaneously activated, triggering neurotropin release and attracting the growth cone toward the synapse. By varying an analog bias called Viuptake, I can control the diffusivity of released neurotropin. Increasing Viuptake decreases the neurotropin diffusion radius, affecting the ability of a synapse to attract its growth cone. Large diffusion radii permit weak attraction of distant growth cones; short diffusion radii permit strong attraction of nearby growth cones. The optimal diffusion radius balances signal strength against signal range.


ID Article Full Text
B Taba and K Boahen, Silicon Growth Cones Map Silicon Retina, Advances in Neural Information Processing Systems 18, B Sholkopf and Y Weiss, Eds, MIT Press, 2006.

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B Taba and K Boahen, Balancing Guidance Range and Strength Optimizes Self-Organization by Silicon Growth Cones, Artificial Neural Networks: Biological Inspirations - ICANN 2005: 15th International Conference, W Duch, J Kacprzyk, E Oja, et al. Eds, LCNS 3697, pp 1027-1034, Springer-Verlag Berlin, 2005.

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B Taba and K Boahen, Topographic Map Formation by Silicon Growth Cones, Advances in Neural Information Processing Systems 15, S Becker, S Thrun, and K Obermayer, Eds, MIT Press, 2003.

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M7 Taba B . Self-Organizing Neuromorphic Systems with Silicon Growth Cones . Doctoral Dissertation, Department of Neuroscience, University of Pennsylvania, Philadelphia, PA, December 2005.
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