A Computer Modeling Approach to Understanding 117 
A computer modeling approach to understanding the 
inferior olive and its relationship to the cerebellar 
cortex in rats 
Maurice Lee and James M, Bower 
Computation and Neural Systems Program 
California Institute of Technology 
Pasadena, CA 91125 
ABSTRACT 
This paper presents the results of a simulation of the spatial relationship 
between the inferior olivary nucleus and folium crus IIA of the lateral 
hemisphere of the rat cerebellum. The principal objective of this 
modeling effort was to resolve an apparent conflict between a proposed 
zonal organization of olivary projections to cerebellar cortex suggested 
by anatomical tract-tracing experiments (Brodal & Kawamura 1980; 
Campbell & Armstrong 1983) and a more patchy organization apparent 
with physiological mapping (Robertson 1987). The results suggest that 
several unique features of the olivocerebellar circuit may contribute to 
the appearance of zonal organization using anatomical techniques, but 
that the detailed patterns of patchy tactile projections seen with 
physiological techniques are a more accurate representation of the 
afferent organization of this region of cortex. 
1 INTRODUCTION 
Determining the detailed anatomical structure of the nervous system has been a major 
focus of neurobiology ever since anatomical techniques for looking at the fine structure 
of individual neurons were developed more than 100 years ago (Ram6n y Cajal 1911). In 
more recent times, new techniques that allow labeling of the distant targets of groups of 
neurons have extended this investigation to include studies of the topographic 
relationships between different brain regions. In general, these so-called "tract-tracing" 
techniques have greatly extended our knowledge of the interrelationships between neural 
structures, often guiding and reinforcing the results of physiological investigations 
(DeYoe & Van Essen 1988). However, in some cases, anatomical and physiological 
techniques have been interpreted as producing conflicting results. One case, considered 
here, involves the pattern of neuronal projections from the inferior olivary nucleus to the 
118 Lee and Bower 
cerebellar cortex. In this paper we describe the results of a computer modeling effort, 
based on the structure of the olivocerebellar projection, intended to resolve this conflict. 
a 
io 
Po 
b 
d 
Figure 1. a: Profile of the mt brain, showing three areas (Cx, cerebral cortex; 
Po, pons; Tr, spinal trigeminal nucleus) that project to the cerebellum (Cb) via 
both climbing fiber (CF) pathways through the inferior olive (IO) and mossy 
fiber (MF) pathways. b: Magnified, highly simplified view of the cerebellar 
cortex, showing a Purkinje cell (P) being supplied with climbing fiber input, 
directly, and mossy fiber input, through the granule cells (G). c: Zonal 
organization of the olivocerebellar projection. Different shading patterns 
represent input from different areas of the inferior olive. Adapted from 
Campbell & Armstrong 1983. Circled area (crus IIA/cms HB) is enlarged in 
Figure ld; bracketed area (anterior lobe) is enlarged in Figure le. d: Detail of 
zonal organization. Dark areas represent bands of Purkinje cells that stain 
positive for monoclonal antibody Zebrin I. According to Grovel et al. 1987, 
these bands have boundaries similar to those resulting from partial tracer 
injections in the inferior olive. Adapted from Gundappa-Sulur et al. 1989. e: 
Patchy organization of the olivocerebellar projection (partial map). Dferent 
shading patterns represent input through the olive from different body surfaces. 
The horizontal and vertical scales are different. Adapted from Logan & 
Robertson 1986. 
A Computer Modeling Approach to Understanding 119 
2 THE OLIVOCEREBELLAR SYSTEM 
Purkinje cells, the principal neurons of the cerebellar cortex, are influenced by two major 
excitatory afferent projections to the cerebellum, the mossy fiber system and the climbing 
fiber system (Palay & Chan-Palay 1973). As shown in Figures la and lb, mossy fibers 
arise from many different nuclei and influence Purkinje cells through granule cells within 
the cortex. Within the cortex the mossy fiber-granule cell-Purkinje cell circuit is 
characterized by enormous divergence (a single mossy fiber may influence several 
thousand Purkinje cells) and convergence (a single Purkinje cell may be influenced by 
several hundred thousand mossy fibers). In contrast, as also shown in Figures la and lb, 
climbing fibers arise from a single source, the inferior olive, and exhibit severely limited 
divergence (10-15 Purkinje cells) and convergence (1 Purkinje cell). 
Because the inferior olive is the sole source of the climbing fiber projection to the entire 
cerebellar cortex, and each Purkinje cell receives only one climbing fiber, the spatial 
organization of the olivocerebellar circuit has been the subject of a large research effort 
(Brodal & Kawamura 1980). Much of this effort has involved anatomical tract-tracing 
techniques in which injections of neuronally absorbed substances are traced from the 
inferior olive to the cerebellum or vice versa. Based on this work it has been proposed 
that the entire cerebellum is organized as a series of strips or zones, oriented in a 
parasagittal plane (Figures lc, ld: Campbell & Armstrong 1983; Gravel et al. 1987). This 
principle of organization has served as the basis for several functional speculations on the 
role of the cerebellum in coordinating movements (Ito 1984; Oscarsson 1980). 
Unfortunately, as suggested in the introduction, these anatomical results are somewhat at 
odds with the pattern of organization revealed by detailed electrophysiological mapping 
studies of olivary projections (Robertson 1987). Physiological results, summarized in 
Figure le, suggest that rather than being strictly zone-like, the olivocerebellar projection 
is organized more as a mosaic of parasagittally elongated patches. 
3 THE MODEL 
Our specific interests are with the tactilely responsive regions of the lateral hemispheres 
of the rat cerebellum (Bower et al. 1981; Welker 1987), and the modeling effort 
described here is a first step in using structural models to explore the functional 
organization of this region. As with previous modeling efforts in the olfactory system 
(Bower 1990), the current model is based on features of the anatomy and physiology of 
the real system. In the following section we will briefly describe these features. 
3.1 ANATOMICAL ORGANIZATION 
Structure of the inferior olive. The inferior olive has a complex, highly folded 
conformation (Gwyn et al. 1977). The portion of the olive simulated in the model 
consists of a folded slab of 2520 olivary neurons with a volume of approximately 0.05 
mm 3 (Figure 2a). 
Afferent projections to the olive. While inputs of various kinds and origins converge 
on this nucleus, we have limited those simulated here to tactile afferents from those 
120 Lee and Bower 
perioral regions known to influence the lateral cerebellar hemispheres (Shambes et al. 
1978). These have been mapped to the olive following the somatotopically organized 
pattern suggested by several previous experiments (Gellman et al. 1983). 
Structure of the cerebellum. The cerebellum is represented in the model by a fiat sheet 
of 2520 Purkinje cells with an area of approximately 2 mm 2 (Figure 2a). Within this 
region, each Purkinje cell receives input from one, and only one, olivary neuron. Details 
of Purkinje cells at the cellular level have not been included in the current model. 
a b 
I I I i 
i t I I I 
Figure 2. a: Basic structure of the model. Folia crus IIA and crus IIB of the 
cerebellum and a cross section of the inferior olive are shown, roughly to scale. 
The regions simulated in the model are outlined. Clusters of neighboring 
olivary neurons project to parasagittal strips of Purkinje cells as indicated. This 
figure also shows simulated correlation results similar to those in Figure lb. b: 
Spatial structure of correlations among records of climbing fiber activity in crus 
IIA. Sizes of filled circles represent cross-correlation coefficients with respect 
to the "master" site (open circle). Sample cross-correlograms are shown for two 
sites as indicated. The autocorrelogram for the "master" site is also shown. 
Adapted from Sasaki et al. 1989. 
3.2 PHYSIOLOGICAL ORGANIZATION 
Spatia!ly correlated patterns of activity When the activities of multiple climbing 
fibers are recorded from within cerebellar cortex, there is a strong tendency for climbing 
fibers supplying Purkinje cells oriented pamsagittally with respect to each other to be 
correlated in their firing activity (Sasaki et al. 1989: Figure 2b). It has been suggested that 
these correlations reflect the fact that direct electrotonic couplings exist between olivary 
neurons CLlin & Yarom 1981a, b; Benardo & Foster 1986). These physiological results 
are simulated in two ways in the current model. First, neighboring olivary neurons are 
electrotonically coupled, thus fh'ing in a correlated manner. Second, small clusters of 
olivary neurons have been made to project to parasagittally oriented strips of Purkinje 
A Computer Modeling Approach to Understanding 121 
cells. Under these constraints, the model replicates the parasagittal pattern of climbing 
fiber activity found in certain regions of cerebellar cortex (compare Figures 2a and 2b). 
Topography of cerebeHar afferents. As diacussed above, this model is intended to 
explore spatial and functional relationships between the inferior olive and the lateral 
hemispheres of the rat cerebellum. Unfortunately, a physiological map of the climbing 
fiber projections to this cerebellar region does not yet exist for the rat. However, a 
detailed map of mossy fiber tactile projections to this region is available (Welker 1987). 
As in the climbing fiber map in the anterior lobe (Robertson 1987; Figure le) and mossy 
fiber maps in various areas in the cat (Kassel et al. 1984), representations of different 
parts of the body surface are grouped into patches with adjacent patches receiving input 
from nonadjacent peripheral regions. On the assumption that the mossy fiber and 
climbing fiber maps coincide, we have based the modeled topography of the olivary 
projection to the cerebellum on the well-described mossy fiber map (Figure 3a). In the 
model, the smoothly varying topography of the olive is transformed to the patchy 
organization of the cerebellar cortex through the projection pathways taken to the 
cerebellum by different climbing fibers. 
a b 
Figure 3. a: Organization of receptive field map in simulated region of crus 
IIA. Different shading patterns represent input from different perioral surfaces. 
b: Simulated tract-tracing experiment. Left, tracer visualization (dark areas) in 
the cerebellum. Right, tracer uptake (dark areas) in the inferior olive. 
122 Lee and Bower 
4 RESULTS: SIMULATION OF ZONAL ORGANIZATION 
Having constructed the model to include each of the physiological features described 
above, we proceeded to replicate anatomical tract-tracing experiments. This was done by 
simulating the chemical labeling of neurons within restricted areas of inferior olive and 
following their connections to the cerebellum. As in the biological experiments, in many 
cases simulated injections included several folds of the olivary nucleus (Figure 3b). The 
results (Figure 3b) demonstrate patterns of labeling remarkably similar to those seen with 
real olivary injections in the rat (compare Figures ld and 3b). 
5 CONCLUSIONS AND FURTHER WORK 
These simulation results have demonstrated that a broadly parasagittal organization can 
be generated in a model system which is actually based on a fine-grained patchy pattern 
of afferent projections. Further, the simulations allow us to propose that the appearance 
of pamsagittal zonation may result from several unusual features of the olivary nucleus. 
First, the folding characteristic of the inferior olive likely places neurons with different 
receptive fields within a common area of tracer uptake in any given anatomical 
experiment, resulting in co-labeling of functionally different regions. Second, the 
tendency for local clusters of olivary neurons to project to parasagittal strips of Purkinje 
cells could serve to extend tracer injection in the parasagittal direction, enhancing the 
impression of parasagittal zones. This is further reinforced by the tendency of the 
patches themselves to be somewhat elongated in the parasagittal plane. Finally, the 
restricted resolution of the anatomical techniques could very well contribute to the overall 
impression of parasagittal zonation by obscuring small, unlabeled regions more apparent 
using physiological procedures. Modeling efforts currently under way will extend these 
results to more than one cerebellar folium in an attempt to account for the appearence of 
transfolial zones in some preparations. 
In addition to these interpretations of previous data, this model also provides both 
directions for further physiological experiments and predictions concerning the results. 
First, the model assumes that mossy fiber and climbing fiber projections representing the 
same regions of the rat's body surface overlap in the cerebellum. We take the similarity 
in modeled and real tract-tracing results (Figures ld and 3b) as suggesting strongly that 
this is, in fact, the case; however, physiological experiments are currently underway to 
test this hypothesis. Second, the model predicts that the parasagittal pattern of climbing 
fiber correlations found in a particular cerebellar region will be dependent on the pattern 
of tactile patches found in that region. Those regions containing large patches (e.g. the 
center of crus IIA) should clearly show parasagittal strips of correlated climbing fiber 
activity. However, in cortical regions containing smaller, more diverse sets of patches 
(e.g. more medial regions of crus IIA), this correlation structure should not be as clear. 
Experiments are also under way to test this prediction of the model. 
A Computer Modeling Approach to Understanding 123 
Acknowledgements 
This model has been constructed using GENESIS, the Caltech neural simulation system. 
Simulation code for the model presented here can be accessed by registered GENESIS 
users. Information on the simulator or this model can be obtained from 
genesiscaltech.bitnet. This work was supported by NIH grant BNS 22205. 
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