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22 Dec Modeling Neural Interconnections

Neuron Branching

Nerve Fibers

The characteristic that distinguishes neurons from other types of cells is that they have things sticking out all over them. This phenomenon is called branching or arborization. While all cells are capable of sprouting appendages like cilia or dendrites, only some actually do. Cells that branch do so for specific reasons that are essential to bio-cybernetic theory and computer modeling of the brain. I’ve examined the literature and made some observations about neurons’ external form, and the nature and extent of neural interconnections. I will also briefly discuss the shape of neurons. I plan to dedicate the next several posts to talking in some detail about neurons, their structure and their internal components. I will explore what may be going on inside neurons as a prelude to the discussion of what goes on between them.

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How Interconnected are We?

A typical neuron makes about ten thousand connections to neighboring neurons. Given the billions of neurons, this means there are as many connections in a single cubic centimeter of brain tissue as there are stars in the Milky Way galaxy” (Eagleman 2012).

The branches of a neuron are axons and dendrites. They are essential to the cybernetic functions of a neuron. Some oft-quoted statements in technical literature dealing with artificial neural networks suggest that most neurons have thousands of connections  [Feldman, 1989, p. 70; Rumelhart & McClelland, 1986, passim & Chapter 20]. As technology advances, we have learned much more about our brain interconnectedness. Actually, the number of connections or synapses differs radically from one cell type to another. The average number is probably well below 1,000 connections per cell. Neurons such as Purkinje cells in the cerebellum and giant pyramidal cells in the cerebrum may have up to tens of thousands of connections. These cells, however, constitute a tiny proportion of the cells in the nervous system. They are orders of magnitude larger than most neurons.

More relevant is the fact that the arborization patterns of these huge cells cover orders of magnitude more cortical geography (space the arborization patterns cover) than most of the cells in the brain. Many relay cells, for instance, cover great distances. Cells that connect the CNS and the ANS through the corticospinal tract possess exceedingly long fibers. Still, in both these examples the number of synapses is relatively small compared to the larger cell types. It is critical that we understand the magnitude of interconnection in the brain. Such a knowledge will be extremely important when it comes time to analyze the integrity of a neuromorphic model. At present, we are not entirely certain of the shape of a neuron in-vivo, except that we know that it has branches and the components pictured here.

Cell types with fewer synapses (input/output) include granule, horizontal, neurogliaform, and cells of Martinotti. Pyramidal and fusiform  (cerebrum), and Purkinje and golgi (cerebellum) cells, have much more complex arborization of neural interconnections.

Cerebellum Layers

Neurons In-Vivo

Neuron in-VivoA neuron is a cell, not altogether unlike a cell in a person’s skin or organ tissue. Cells also exist in all other biological things, from tree’s bark to a dog’s trunk (though not in a dog’s bark). Until recently, we’ve assumed that in-vitro (stored in lab containers) samples of cells such as neurons had about the same shape as they did in-vivo (before being removed from the living organism). This is actually a difficult assumption to support because of the known tendency of biological tissues to change shape when exposed to a foreign environment. The membranes that serve as the skin of cells are far more sensitive than our epidermis. When exposed in-vitro to foreign chemicals, or even to water, they may become tense, like a cat that is frightened or poised to strike. After the illustration at right in which a neuron is pictured as a kind of shapeless blob, the neuron pictured above looks quite shapely.

Microscopic (and smaller) artifacts are now accessible through advanced electron microscopy. Laser technologies have enabled scientists to get ever-thinner slices of cells that yield more interesting information. Advanced staining techniques have been developed to divulge the chemical structures of intracellular components. Innovative approaches to simulation of in-vivo conditions have helped scientists observe life-like phenomena in the laboratory.

Branching Fibers

By slicing cells into lots of cross-sections and using computer analysis to reconstruct them, scientists have shown that in-vivo neurons may have a radically different shape than had been assumed in the past. Or is it possible that they are amorphous at rest and assume a different posture when stimulated? These questions about external form, neurons’ shapes and branching patterns, are important considerations in modeling neuromorphic computing. Internal form and components are important as well. In the next posts, I will probe inside neurons looking for the micro-components of cognition.

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