Brain size and number of neurons: an exercise in synthetic neuroanatomy.

Certain remarkable invariances have long been known in comparative neuroanatomy, such as the proportionality between neuronal density and the inverse of the cubic root of brain volume or that between the square root of brain weight and the cubic root of body weight. Very likely these quantitative relations reflect some general principles of the architecture of neuronal networks. Under the assumption that most of brain volume is due to fibers, we propose four abstract models: I, constant fiber length per neuron; II, fiber length proportionate to brain diameter; III, complete set of connections between all neurons; IV, complete set of connections between compartments each containing the square root of the total number of neurons. Model I conforms well to the cerebellar cortex. Model II yields the observed comparative invariances between number of neurons and brain size. Model III is totally unrealistic, while Model IV is compatible with the volume of the hemispheric white substance in different mammalian species.

Geometry of orientation columns in the visual cortex.

The optimal direction of lines in the visual field to which neurons in the visual cortex respond changes in a regular way when the recording electrode progresses tangentially through the cortex (Hubel and Wiesel, 1962). It is possible to reconstruct the field of orientations from long, sometimes multiple parallel penetrations (Hubel and Wiesel, 1974; Albus, 1975) by assuming that the orientations are arranged radially around centers. A method is developed which makes it possible to define uniquely the position of the centers in the vicinity of the electrode track. They turn out to be spaced at distances of about 0.5 mm and may be tentatively identified with the positions of the giant cells of Meynert.

Shapes and sizes of different mammalian cerebella. A study in quantitative comparative neuroanatomy.

The shape of the cerebellar cortex in fourteen mammalian species and one bird was studied by careful dissection, counts of the numbers of folia, and measurement of their length. All mammalian cerebella conformed to the same general plan, with an anterior region where folia are continuous between right and left, and three separate posterior appendages. There were, however, considerable differences between species, both in the relative length of the posterior appendages and in the relative abundance of folia on the midline compared to the lateral portions. In order to discover general laws referring to the width and length of the cerebellar cortex in their relation to body weight, cerebellar weight, and area of cerebellar cortex, an allometric analysis was performed. By plotting the values for the various species on log-log diagrams, the following statements can be inferred: 1. The weight of the cerebellar cortex is proportionate to the body weight to the power of 0.72, well comparable to the classical proportionality between brain weight and body weight to the power of 2/3 (Jerison 1973). 2. Cerebellar area and cerebellar weight are proportionate in larger animals, but in the smaller species the thickness of the cerebellar cortex varies and therefore a different dependence is valid. 3. The width of the cerebellar cortex increases with body size in the smaller species but tends to remain constant in the larger ones. 4. The longest anterior-posterior extension in our collection was measured in the bovine cerebellum. 5. The position of man in our collection of species is particular in several ways. The width of the human cerebellum is far greater than allometric relations established for the other species would suggest. Also, the vermal length of man falls short of the allometric rule established for the other species.

[Model of a neurological theory of speech]. / Entwurf einer neurologischen Theorie der Sprache.

Recently, theories of neuronal computation in the brain have become detailed enough, so that it becomes possible to speculate about mechanisms underlying the production and perception of language. How many neurons are involved when we utter, or understand, a word, a phoneme, a phrase? In what neuronal form are the rules of grammar laid down in the synaptic network? To what does a morpheme correspond in the brain?

Some peculiar synaptic complexes in the first visual ganglion of the fly, Musca domestica.

In the lamina ganglionaris, the first optic ganglion of the fly, the inventory of cell types as well as the patterns of their connections are well known from light microscopic investigations. Even the synaptic contacts are known with relative completeness. However, the structural details visible on electron micrographs are very difficult to interpret in functional terms. This paper concentrates on two aspects: 1) the synaptic complex between a retinula cell axon and four postsynaptic elements, arranged in a constant elongated array (it is suggested that all synapses in which the retinula cell is presynaptic are of this kind), and 2) the "gnarl" complex in which a presynaptic specialization in one neuron is separated from another neuron by a complicated glial invagination. The participation of glia at postsynaptic sites seems to be quite common in this ganglion. Occasionally it seems that a glia cell is the only postsynaptic partner facing a presynaptic specialization within a neuron.

The detection and generation of sequences as a key to cerebellar function: experiments and theory.

Starting from macroscopic and microscopic facts of cerebellar histology, we propose a new functional interpretation that may elucidate the role of the cerebellum in movement control. The idea is that the cerebellum is a large collection of individual lines (Eccles's "beams": Eccles et al. 1967a) that respond specifically to certain sequences of events in the input and in turn produce sequences of signals in the output. We believe that the sequence-in/sequence-out mode of operation is as typical for the cerebellar cortex as the transformation of sets into sets of active neurons is typical for the cerebral cortex, and that both the histological differences between the two and their reciprocal functional interactions become understandable in the light of this dichotomy. The response of Purkinje cells to sequences of stimuli in the mossy fiber system was shown experimentally by Heck on surviving slices of rat and guinea pig cerebellum. Sequential activation of a row of eleven stimulating electrodes in the granular layer, imitating a "movement" of the stimuli along the folium, produces a powerful volley in the parallel fibers that strongly excites Purkinje cells, as evidenced by intracellular recording. The volley, or "tidal wave," has maximal amplitude when the stimulus moves toward the recording site at the speed of conduction in parallel fibers, and much smaller amplitudes for lower or higher "velocities." The succession of stimuli has no effect when they "move" in the opposite direction. Synchronous activation of the stimulus electrodes also had hardly any effect. We believe that the sequences of mossy fiber activation that normally produce this effect in the intact cerebellum are a combination of motor planning relayed to the cerebellum by the cerebral cortex, and information about ongoing movement, reaching the cerebellum from the spinal cord. The output elicited by the specific sequence to which a "beam" is tuned may well be a succession of well timed inhibitory volleys "sculpting" the motor sequences so as to adapt them to the complicated requirements of the physics of a multijointed system.