Anatomically Accurate Neural Networks: Building a Hippocampus
Can virtual neurons be assembled in realistic neural networks, and can these be used to study the electrophysiological behavior at the system level? Steve Senft has developed a program, called ArborVitae (AV), that implements stochastic and statistical algorithms similar to those described for L-Neuron at a population level.
As an example of the ArborVitae output, here we show the main cells of the rat hippocampus. In each panel, the upper four neurons are real cells from the Southampton archive. The lower four neurons are created with AV. Axons are not present in any of the cells. Each of the AV cell has only approximately 1/10 of the dendritic compartments of a corresponding real neuron. Upper left panel: CA3 pyramidal cells. Color code: basal dendrites are brown (receiving inputs from gabaergic interneurons, cholinergic septohippocampal pathway and glutamatergic Schaffer collaterals), proximal apical dendrites are green (receiving inputs from gabaergic interneurons, glutamatergic mossy fibers and Schaffer collaterals), distal apical dendrites are blue (receiving inputs from gabaergic interneurons, glutamatergic perforant pathway and Schaffer collaterals). In the real AV model the distal apical dendrites are more sharply oriented towards the top (away from the basal dendrites). Here this effect is diluted by the lower density of basal dendrites (only four neurons are present!). Upper right panel: CA1 pyramidal cells. Color code: basal dendrites are brown (receiving inputs from gabaergic interneurons, cholinergic septohippocampal pathway and glutamatergic CA1 axonal collaterals), apical dendrites are green (receiving inputs from gabaergic interneurons and glutamatergic Schaffer collaterals). Lower left panel: DG granule cells. The dendrites receive their inputs from gabaergic and glutamatergic interneurons, cholinergic septohippocampal pathway and glutamatergic perforant pathway. Lower right panel: polymorphic cells. This stellate-like structure is adopted by several neuronal families such as GPC and mossy cells in DG, Oriens interneurons in CA3 and Alveus interneurons in CA1.
ArborVitae also implements an algorithm to describe axonal navigation and synaptic connectivity. We took advantage of this feature to generate a virtual, small-scale model of a hippocampal slice. This structure consists of the dentate gyrus granule cell layer (bottom right in the figure), the CA3 and CA1 pyramidal cell layers (left and top right in the figure, respectively), as well as an off-field "black-box" entorhinal cortical module sending axons to the granule cells and receiving axons from CA1, and a septohippocampal input to CA3. Because this network is interconnected, we were able to simulate a simple form of electrical transmission (white colors indicate depolarized membranes). We are now working on a larger-scale model of the hippocampal slice. If you want to learn more, please see our technical report "Computational Neuroanatomy of the Hippocampus".Our interest in the hippocampus is motivated by several reasons: [A] The hippocampus is involved in associative learning, one of the basic building blocks of mammalian higher cognitive functions. [B] The rat hippocampus is among the best known neuroanatomical structures, and morphological data are extensively available in the scientific literature. [C] The hippocampus has a mainly lamellar structure, therefore an entire hippocampus can be assembled by stacking together many slices. In other words, the system is easily scalable up in the computational model. We ran an extensive literature search of the cellular connectivity of the rat hippocampus, and this is the basis of our larger scale anatomical model.
The hippocampal formation (upper panel, adapted from Schultz et al., 1998): The entorhinal cortex (EC), modeled as black box columns, sends perforant pathway fibres (PP) to the dentate gyrus (DG) and to CA3. DG granule cells output mossy fibres (MF) to CA3. CA3 pyramidal cells send axons recurrently into CA3 and to CA1 through the Schaffer collaterals (SC). CA1 pyramidal cells project back to EC (and to the subicular complex, not modeled). Principal cells of DG, CA3 and CA1 also receive cholinergic input from the medial septal complex (not modeled) via the septo-hippocampal pathway (SHP), modeled as a synchronous input. All the cells and the connections within DG, CA3 and CA1 will be modeled in detail (lower panel): the flat scheme of the hippocampus shows the different layers. The DG is divided into hilus/polymorphic layer (H), granule cell layer (G), and molecular layer/fascia dentata (M), which contains the granule cell dendrites. The CA fields are divided into lacunosum layer/stratutm radiatum (L), which contains the pyramidal cell basal dendrites, pyramidal cell layer, and alveus/stratum radiatum (A), which contains the pyramidal cell apical dendrites. The neurons that will be modeled, specified in each layer of the bottom panel, are reported below (each hyperlinked to its synaptic matrix), along with the estimated number of cells (Patton and McNaughton, 1995; Bernard and Wheal, 1994).
Dentate Gyrus (DG): CA3: CA1:
106 gc (granule
2x105 pc (ca3 pyramidal cells)
3x105 pc (ca1 pyramidal)
3x104 mc (mossy cells) 4x103 ri (radiatum interneurons) 4x103 bc (ca1 basket)
1.5x104 gpc (gabaergic polymorphic cells) 4x103 oi (oriens interneurons) 4x103 lm (lacunoso-moleculare)
104 bc (dg basket cells) 103 cc (ca3 chandelier cells) 4x103 oa (oriens-alveus)
104 mopp (molecular layer perforant path cells) 103 cc (ca1 chandelier)
103 cc (dg axoaxonic chandelier cells)
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