Granule

Overview

(adapted from: https://en.wikipedia.org/wiki/Cerebellar_granule_cell):

Cerebellar granule cells form the thick granular layer of the cerebellar cortex and are among the smallest neurons in the brain. (The term granule cell is used for several unrelated types of small neurons in various parts of the brain.) Cerebellar granule cells are also the most numerous neurons in the brain: in humans, estimates of their total number average around 50 billion, which means that they constitute about 3/4 of the brain’s neurons.

The cell bodies are packed into a thick granular layer at the bottom of the cerebellar cortex. A granule cell emits only four to five dendrites, each of which ends in an enlargement called a dendritic claw. These enlargements are sites of excitatory input from mossy fibers and inhibitory input from Golgi cells.

The thin, unmyelinated axons of granule cells rise vertically to the upper (molecular) layer of the cortex, where they split in two, with each branch traveling horizontally to form a parallel fiber; the splitting of the vertical branch into two horizontal branches gives rise to a distinctive “T” shape. In humans, a parallel fiber runs for an average of 3 mm in each direction from the split, for a total length of about 6 mm (about 1/10 of the total width of the cortical layer). As they run along, the parallel fibers pass through the dendritic trees of Purkinje cells, contacting one of every 3–5 that they pass, making a total of 80–100 synaptic connections with Purkinje cell dendritic spines.[1] Granule cells use glutamate as their neurotransmitter, and therefore exert excitatory effects on their targets.

See Microcircuit of Cerebellar cortex for a diagram of grannule cells.

Density

In cat:

A percentage of 41.85% of the total volume of the granular substance was occupied by the granule cells (bodies), their density calculated for the living state being 2.8 x 10^6/cu.mm. [PalkovitsM+2-1971b] p. 29.

In rat:

Using morphological measurements, it can be calculated that the rat cerebellar granular layer has a cell density of 4 × 10^6/mm^3 for granule cells and 9300/mm^3 for Golgi cells, with a Golgi cell : granule cell ratio of 1:430 (Korbo et al., 1993). Moreover, the density of the glomeruli is 3 × 10^5/mm^3, and each glomerulus is composed of one mossy fiber terminal, about 53 dendrites from separate granule cells (Jakaband Hamori, 1988), and one or more dendrites from Golgi cells. [DAngeloE+5-2013] p. 9-10.

Quantity

In cat:

The granular layer contributed to 29.09% of the total cerebellar volume, their absolute number being 2.2 x 10^9. [PalkovitsM+2-1971b] p. 29.

This value is used in [LoebnerEE-1989] (the value is probably from the same source, e.g. [PalkovitsM+2-1971b]).

The granule cell : Purkinje cell ratio was 1700-1800. [PalkovitsM+2-1971b] p. 29.

See Table 2 in note for [LangeW-1975] for granule cell : Purkinje cell ratio for different species.

Connection to Purkinje Cells

Structure

In cat:

From: [PalkovitsM+2-1972]:

Numerically, the granule cells belonging to one Purkinje cell (1,792) are capable of transmitting impulses from 4 mossy fibers and their 68 rosettes (glomeruli), while the parallel fibers, being 2 mm long, penetrate the dendrite trees of 225 Purkinje cells. Since they establish synapses with only every fifth of these Purkinje cells, the calculated number of parallel fibers-Purkinje spine synapses would be 80,550/ Purkinje cell 11. This calculated value agrees reasonably well with the counted number of Purkinje cell dendritic spines = 91,600.

Each granule call split to form a “T” to form parallel fibers that extend 1 mm (2 mm total) in a direction parallel to the longititudional access of the folium (that is in a direction perpendicular to the Purkinje cells).

Divergence

Cat: 45.

From: [PalkovitsM+2-1972], p. 27: The parallel fibers divide in T-fashion and run in both directions for an average distance of 1 mm, i.e. they are 2 mm long n. They establish synapses with only about every fifth Purkinje cell whose dendritic tree they cross. With 225 Purkinje cell dendritic trees accommodated in 2 mm along the longitudinal axis of the folium 9, each parallel fiber may contact synaptically 45 Purkinje cells.

This is different from the value given in Fig. 2 of [LoebnerEE-1989], which is 200 * 10^3. I’m not sure what that figure is referring to.

Convergence

Cat: 80,550

From: [PalkovitsM+2-1972] Since they establish synapses with only every fifth of these Purkinje cells, the calculated number of parallel fibers-Purkinje spine synapses would be 80,550/ Purkinje cell [PalkovitsM+2-1971c]. This calculated value agrees reasonably well with the counted number of Purkinje cell dendritic spines = 91,600.

This is similar to the value in [LoebnerEE-1989] Fig. 2 (8.5 x 10^4). I’m not sure what the source is of that value.

Connection to Golgi Cells

Divergence

Unknown ([LoebnerEE-1989], Fig. 2)

Convergence

5.2 x 10^3 ([LoebnerEE-1989], Fig. 2)

Connection to Basket Cells

Divergence

Unknown ([LoebnerEE-1989], Fig. 2)

Convergence

3.7 x 10^3 ([LoebnerEE-1989], Fig. 2)

Connection to Stellate Cells

Divergence

Unknown ([LoebnerEE-1989], Fig. 2)

Convergence

3.6 x 10^3 ([LoebnerEE-1989], Fig. 2)

Data for table Cells and connections in cat

The following table has data and references for table Cells and connections in cat. Values are either a Cell count, or FO,FI where FO is fan-out (number of target cells each source cell contacts) and FI is fan-in (number of source cells going to each target cell).

Id	Source cell	Target cell	Value	Reference
r1	granule	Cell count	2.2x10^9	[LoebnerEE-1989] 1
r2	granule	basket	?, 3.7x10^3	[LoebnerEE-1989] 1
r3	granule	golgi	?, 5.2x10^3	[LoebnerEE-1989] 1
r4	granule	purkinje	200x10^3, 8.5x10^4	[LoebnerEE-1989] 1
r5	granule	stellate	?, 3.6x10^3	[LoebnerEE-1989] 1

1(1,2,3,4,5)

EE Loebner. Intelligent network management and functional cerebellum synthesis. In Raugh MR, editor, Cerebellar Models of Associative Memory: Three papers from IEEE COMPCON SPRING ‘89, pages 14–19. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1989. PDF: LoebnerEE-1989.pdf, Notes: LoebnerEE-1989.html.