Mouse cerebellar cortex configuration

Introduction

The mouse folder contains the configurations for the reconstruction and simulation of the mouse cerebellar cortex with BSB.

These reconstructions are based on the iterative work of many researchers distributed in many papers. The role of this file is to make explicit the origin of each value and strategy extracted from the literature and integrated into these configurations. All the configurations present in this folder are based on the mouse_cerebellar_cortex.yaml file. It corresponds to the configuration file written for the reconstruction of the cerebellar circuit presented in the De Schepper et al. (2022) [1] paper. This circuit configuration will be later referred to as the canonical circuit.

We will follow the structure of the BSB configuration files to present each of their sections and the data they leverage.

Biological context

The cerebellar cortex is a subregion of the cerebellum structured as a folded sheet. This cortical sheet is itself decomposed into 2 major layers: the granular layer and the molecular layer, separated by a thin sheet of Purkinje cells, representing the Purkinje layer. Each layer contains its own cell types composition, placement rules and connectivity strategies. Fig. 1 shows the different cell type present in the network and their connections.

Abbreviations: mf (Mossy fibers); glom (Glomeruli); UBC (Unipolar brush cells); GrC (Granule cells); GoC (Golgi cells); PC (Purkinje cells); aa (Ascending axons); pf (Parallel fibers); BC (Basket cells); SC (Stellate cells); IO (Inferior olive); cf (Climbing fibers); DCN (Deep cerebellar nuclei).

For most of the configurations available here, only a portion of the cerebellar cortex is built in a cubic volume with fixed layer thicknesses, to simplify the orientation and scaling of neuronal geometrical representation (morphologies) but also to limit the number of neurons and therefore the final size of the network.

Keep in mind that the default configurations do not include every cell type (and therefore connections) displayed in this Figure.

In the mouse canonical circuit case, the UBC, DCN, IO and related connections are not included.

Circuit configuration

Coordinate framework

By convention, the circuit is oriented so that its layers are stacked vertically with the granular layer at the bottom and the molecular layer at the top. We derived a coordinate framework (x,y,z) from this layout, based on the right-hand orientation convention. Its origin is set at the bottom of the circuit, the z axis pointing to the top of the molecular layer. The (y-z) plane corresponds to the para-sagittal sections that are co-planar with the Purkinje dendritic trees and normal to the granule cells parallel fibers. Finally, unit of distance in the configurations are expressed in micrometers \(\mu m\). Note that the morphologies provided are oriented by default to match this convention.

Network dimensions

The canonical circuit is built in a cubic volume of \(300 \times 200 \times 295\) \(\mu m^3\) in the (x,y,z) convention (see network, regions and partitions in the configuration). The thickness of each of its layer has been determined according to literature findings and to match the size and shape of the available morphologies:

• The Purkinje layer corresponds to a one cell thick sheet of Purkinje cells. The Purkinje cell soma diameters determine therefore the thickness of this layer. According to Hendelman & Aggerwal (1980) [2], Purkinje cell’s soma diameters have been estimated to less than \(20 \mu m\) in mice. We chose here \(15 \mu m\).

• The molecular layer total thickness has been calculated to fit the size of the dendritic arborization of the Purkinje cell’s morphology as \(150 \mu m\). The molecular layer is itself divided in the canonical circuit into two sub-layers based on their neuronal composition. Here, the bottom part of the molecular layer (hence the part stacked right on top of the Purkinje layer) contains the Basket cells (b_molecular_layer in the configuration); while the top part hold the Stellate cells (s_molecular_layer). In fact, according to literature data (J. Kim & Augustine, 2021 [3]; Sultan & Bower, 1998 [4]), SCs are more likely located in the outer two-third of the Molecular layer. While this distribution of cells is closer to gradient in real mice, we assumed a clear separation between the populations. The basket layer is therefore \(50 \mu m\) thick while the stellate layer is \(100 \mu m\) thick.

• The granular layer’s thickness has been similarly fitted to match the size of the Golgi cell basal dendritic tree, here \(130 \mu m\). Note that the size of the granule cell ascending axons have been set to this constraint.

Cellular composition

The cellular composition of the circuit is determined in the cell_types section of the configuration file. Each cell type is linked here to a partition in the circuit, and a morphology is assigned. Additionally, we introduce here two components used to innervate the circuit: the mossy fibers originating from various other brain regions, and the glomeruli that form at their terminals. These components are used as building entities to relay stimuli from other regions into the circuit and have therefore no morphology attached.

We will describe here the spatial parameters used in canonical circuit:

Layer	Cell name	Type	Radius (\(\mu m\))	Density (\(\mu m^{-3}\))	References
Granular layer	Glomerulus (glom)	Exc.	1.5	0.0003	Solinas et al. (2010) [5]
Granular layer	Mossy fibers (mf)	Exc.	/	count relative to glom. ratio=0.05	Billings et al. (2014) [6]
Granular layer	Granule Cell (GrC)	Exc.	2.5	0.0039	Casali et al. (2019) [7]
Granular layer	Golgi Cell (GoC)	Inh.	4.0	0.000009	Casali et al. (2019) [7]
Purkinje layer	Purkinje cell (PC)	Inh.	7.5	planar density: 0.001166	Keller et al. (2018) [19]
Molecular layer	Basket cell (BC)	Inh.		0.00005	Casali et al. (2019) [7]
Molecular layer	Stellate cell (SC)	Inh.		0.00005	Casali et al. (2019) [7]

Warning

Note that most literature data in this table comes from rat data.

The density of glom have been calculated in Solinas et al. (2010) [5] based on the glomerulus to granule convergence and divergence ratios (derived from values in Korbo et al., 1993 [8] and Jakab and Hámari, 1988 [9]).

For PC cells, the planar density was calculated to obtain approximately 70 PC in our Purkinje Layer, which results in a planar density of 1166 \(PCs/mm^{2}\). This density is consistent with the data from Keller et al. [19]

The densities of GrC, GoC, BC and SC are reported in Table 1 of Casali et al. (2019) [7]. The authors cite Korbo et al. (1993) [8] for the values in this table, however, no equivalent was found in the cited paper. These values might have been optimized to improve simulation results. They could also have been obtained through geometric constrained placement to minimize the overlap of somas.

Neuron Morphologies configurations

[TODO: Add explanation on morphologies origin here.]

Placement

Except for Purkinje cells (PC), every entity is supposed to be uniformly distributed in their own layer.The bsb RandomPlacement strategy is chosen here to place them. In short, this strategy chose a random position for each entity within their sub-partition. Note that this does not take into account any potential overlapping of cells’ soma unlike ParticlePlacement strategies. However, comparative analysis conducted in our laboratory have shown that the latter strategy have a limited impact on connectivity and simulation results, while the computational cost of checking soma overlapping is not negligible.

PC are placed in arrays, \(130 \mu m\) apart from each other along the para-sagittal plane (xz) to guarantee that their dendritic arborizations do not overlap. Furthermore, each row of PC somas is shifted with respect to its predecessor to form a 80 degree angle on the (xy) plane.

Connectivity

The following table list all the connections present in the model. The connection id of the first column corresponds to the numbers reported in Fig. 1.

Table 1 Connectivity rules of the cerebellar cortex circuit

#	Source Name	Source Branch	Target Name	Target Branch	Strategy	References
1	mf	/	glom	/	ConnectomeMossyGlomerulus	Sultan (2001) [10]
2	glom	/	GrC	dendrites	ConnectomeGlomerulusGranule	Houston et al. (2017) [12]
3	glom	/	GoC	basal dendrites	ConnectomeGlomerulusGolgi	Kanichay and Silver (2008) [11]
4	GoC	axon	GrC	same as through glom	ConnectomeGolgiGlomerulus	Barmack and Yakhnitsa (2008) [13]
5	GoC	axon	GoC	basal dendrites	VoxelIntersection	Hull and Regehr (2012) [14]
6	GrC	ascending axon	GoC	basal dendrites	VoxelIntersection	Cesana et al. (2013) [15]
7	GrC	parallel fiber	GoC	apical dendrites	VoxelIntersection	Kanichay and Silver (2008) [11]
8	GrC	ascending axon	PC	ascending axon targets	VoxelIntersection	Wang and Huang (2006) [16]
9	GrC	parallel fiber	PC	parallel fiber targets	VoxelIntersection	Wang and Huang (2006) [16]
10	GrC	parallel fiber	BC	dendrites	VoxelIntersection	Jörntell et al. (2010) [17]
11	GrC	parallel fiber	SC	dendrites	VoxelIntersection	Jörntell et al. (2010) [17]
12	BC	axon	PC	soma	VoxelIntersection	Jörntell et al. (2010) [17]
13	SC	axon	PC	stellate cell targets	VoxelIntersection	Jörntell et al. (2010) [17]
14	BC	axon	BC	dendrites	VoxelIntersection	Ito (2013) [18]
15	SC	axon	SC	dendrites	VoxelIntersection	Ito (2013) [18]

Parameters explanation:

We currently have no morphologies for the mf and glom, which makes it impossible to use fiber or voxel intersection techniques to implement their related connection rules. We therefore simplified the geometry of the neurites involved in these connections.

Sultan provides ranges of distance between gloms and their respective mf in their paper [10]: \(57.6 \pm 60 \times 19.6 \pm 18.8 \mu m\) along respectively the x and y axes in our coordinate system. In our model, we used the rounded mean values as the maximum distance between mf and their gloms.

GrC of the adult mouse cerebellar cortex has \(3.9 \pm 0.1\) dendrites that spreads for \(~40 \mu m\) in each direction, as reported in Houston et al. (2017) [12] (see Figure 2G). In our model, we therefore assumed that each GrC has 4 dendrites of \(40 \mu m\), to match also the number of branches of the respective morphology. These values are used in the glom to GrC connectivity rule. The convergence value of this connection pair is set here to the number of dendrites.

GoC basolateral arborizations spread across \(100 \mu m\) in P25 rat according to Kanichay and Silver (2008) [11]. This has been simplified to a sphere of \(50 \mu m\) radius surrounding their soma for the GoC to glom connectivity.

Barmack and Yakhnitsa (2008) [13] reported that the mean mediolateral extent of the GoC axon is \(180 \pm 40 \mu m\), and that it spreads along the parasagittal plane. In our connection from GoC to GrC (through glom), we used a \(150 \mu m\) sphere surrounding the GoC soma to find potential glom targets. The maximum number of glom target (divergence) for each GoC was set to 40 in Solinas et al. (2010) [5]. However, the rationale behind this particular value is unclear but probably to balance the granular layer excitation and inhibition.

For the rest of the connection rules, we leveraged each neuron morphologies to detect appositions of their neurites. Fiber intersection methods require a lot of computational power. For this reason, we used BSB VoxelIntersection strategy, as it simplifies this detection representing morphologies using voxels.

The affinity and distributions of contact points parameters of these connections were tuned to match connectivity divergence and convergence values from De Schepper et al. (2022) [1].

We introduce a correction for the SC-PC connectivity which consists in a normal distribution of synapse points per SC-PC connections (parameters loc = 10, scale = 0.3). The idea was to have ~50 afferent synapses per PC to match the range of inhibition efficiency described in Rizza et al. 2021 [20]

Extensions to the canonical model

The canonical circuit serves as a template for cerebellar cortex reconstructions. Extensions can be combined to the model to include specific details and perform various simulations.

See the Extra cell types section to see the additional cell types available as extensions of the canonical circuit.

See also the different simulation parameters and paradigm available for NEST simulations and Neuron simulations.

References

[1] (1,2)

De Schepper, R., Geminiani, A., Masoli, S., Rizza, M. F., Antonietti, A., & Casellato, C. (2022). Model simulations unveil the structure-function-dynamics relationship of the cerebellar cortical microcircuit. Communications Biology, 5(1), 1-19. https://doi.org/10.1038/s42003-022-04213-y

[2]

Hendelman, W. J., & Aggerwal, A. S. (1980). The Purkinje neuron: I. A Golgi study of its development in the mouse and in culture. Journal of Comparative Neurology, 193(4), 1063–1079. https://doi.org/10.1002/cne.901930417

[3]

Kim, J., & Augustine, G. J. (2021). Molecular Layer Interneurons: Key Elements of Cerebellar Network Computation and Behavior. Neuroscience, 462, 22-35. https://doi.org/10.1016/j.neuroscience.2020.10.008

[4]

Sultan, F., & Bower, J. M. (1998). Quantitative Golgi study of the rat cerebellar molecular layer interneurons using principal component analysis. Journal of Comparative Neurology, 393(3), 353-373. PMID: 9548555. https://doi.org/10.1002/(SICI)1096-9861(19980413)393:3<353::AID-CNE7>3.0.CO;2-0

[5] (1,2,3)

Solinas, S., Nieus, T., & D‘Angelo, E. (2010). A realistic large-scale model of the cerebellum granular layer predicts circuit spatio-temporal filtering properties. Frontiers in cellular neuroscience, 4, 903. doi: 10.3389/fncel.2010.00012. PMID: 20508743; PMCID: PMC2876868.

[6]

Billings, G., Piasini, E., Lőrincz, A., Nusser, Z., & Silver, R. A. (2014). Network structure within the cerebellar input layer enables lossless sparse encoding. Neuron, 83(4), 960-974. https://doi.org/10.1016/j.neuron.2014.07.020

[7] (1,2,3,4,5)

Casali, S., Marenzi, E., Medini, C., Casellato, C., & D’Angelo, E. (2019). Reconstruction and simulation of a scaffold model of the cerebellar network. Frontiers in neuroinformatics, 13, 444802.https://doi.org/10.3389/fninf.2019.00037

[8] (1,2)

Korbo, L., Andersen, B. B., Ladefoged, O., & Møller, A. (1993). Total numbers of various cell types in rat cerebellar cortex estimated using an unbiased stereological method. Brain research, 609(1-2), 262-268. https://doi.org/10.1016/0006-8993(93)90881-M

[9]

Jakab, R. L., & Hamori, J. (1988). Quantitative morphology and synaptology of cerebellar glomeruli in the rat. Anatomy and embryology, 179, 81-88. https://doi.org/10.1007/BF00305102

[10] (1,2)

Sultan, F. (2001). Distribution of mossy fibre rosettes in the cerebellum of cat and mice: Evidence for a parasagittal organization at the single fibre level. European Journal of Neuroscience, 13(11), 2123-2130. https://doi.org/10.1046/j.0953-816x.2001.01593.x

[11] (1,2,3)

Kanichay, R. T., & Silver, R. A. (2008). Synaptic and cellular properties of the feedforward inhibitory circuit within the input layer of the cerebellar cortex. Journal of Neuroscience, 28(36), 8955-8967. https://doi.org/10.1523/JNEUROSCI.5469-07.2008

[12] (1,2)

Houston, C. M., Diamanti, E., Diamantaki, M., Kutsarova, E., Cook, A., Sultan, F., & Brickley, S. G. (2017). Exploring the significance of morphological diversity for cerebellar granule cell excitability. Scientific Reports, 7(1), 1-16. https://doi.org/10.1038/srep46147

[13] (1,2)

Barmack, N. H., & Yakhnitsa, V. (2008). Functions of interneurons in mouse cerebellum. Journal of Neuroscience, 28(5), 1140-1152. https://doi.org/10.1523/JNEUROSCI.3942-07.2008

[14]

Hull, C., Regehr, W. G. (2012). Identification of an inhibitory circuit that regulates cerebellar Golgi cell activity. Neuron, 73(1), 149-158. https://doi.org/10.1016/j.neuron.2011.10.030

[15]

Cesana, E., Pietrajtis, K., Bidoret, C., Isope, P., D’Angelo, E., Dieudonné, S., & Forti, L. (2013). Granule cell ascending axon excitatory synapses onto Golgi cells implement a potent feedback circuit in the cerebellar granular layer. Journal of Neuroscience, 33(30), 12430-12446. https://doi.org/10.1523/JNEUROSCI.4897-11.2013

[16] (1,2)

Wang, L., & Huang, R. H. (2006). Cerebellar granule cell: Ascending axon and parallel fiber. European Journal of Neuroscience, 23(7), 1731-1737. https://doi.org/10.1111/j.1460-9568.2006.04690.x

[17] (1,2,3,4)

Jörntell, H., Bengtsson, F., Schonewille, M., & De Zeeuw, C. I. (2010). Cerebellar molecular layer interneurons–computational properties and roles in learning. Trends in neurosciences, 33(11), 524-532.https://doi.org/10.1016/j.tins.2010.08.004

[18] (1,2)

Ito, M. (2013). Cerebellar Microcircuitry. Reference Module in Biomedical Sciences. https://doi.org/10.1016/B978-0-12-801238-3.04544-X

[19] (1,2)

Keller, D. (2018). Cell Densities in the Mouse Brain: A Systematic Review. Frontiers in Neuroanatomy, 12. https://doi.org/10.3389/fnana.2018.00083

[20]

Rizza, M. F., Locatelli, F., Masoli, S., Sánchez-Ponce, D., Muñoz, A., Prestori, F., & D’Angelo, E. (2021). Stellate cell computational modeling predicts signal filtering in the molecular layer circuit of cerebellum. Scientific Reports, 11(1), 3873. https://doi.org/10.1038/s41598-021-83209-w