A computer model of the cerebellar cortex of the frog.

A computer simulation of the neuronal circuits in the cerebellar cortex of frog is developed as a means of testing the functional properties of this cortex. The model is based on present day information regarding morphology and function of the different cortical neurons. In order to allow the model to resemble as closely as possible the actual cerebellum, the model was grown by-the computer to simulate data obtained from anatomical studies of the different elements. The model comprises a Purkinje cell layer consisting of 8285 Purkinje ceils, 1.68 million granule cells, and 16,820 mossy fibers. Their connectivity was specified on the basis of probability density functions based on the spatial organization of these different elements. Once the cerebellar model was assembled, computer results indicated that the mossy fiber/granule cell system displayed functional specificities which were not expected a priori. (1) A spatially localized mossy fiber input in the peduncle generated localized activation in the cells of the granular layer despite the stochastic nature of the connectivity. This activation of the granular layer occurred in a spindle-like manner which tended to be localized in particular depths in the granular layer. (2) Simultaneous activation of several discrete points in the peduncle, rather than producing a diffuse activity in the granular layer, generated distinct activation of sets of neurons in this layer. In conclusion the model gives evidence for functional specificity in the absence of morphological specificity. This finding suggests that only a limited amount of genetic specificity may be necessary to generate functional specificity in certain neuronal circuits. IN VIEW of the increased amount of detailed information about cerebellar anatomy and physiology provided in recent years (ECCLES, ITO & SZENT~~THAI, 1967; LLINAS, 1969; PALAY & CHAN-PALAY, 1974), it has become correspondingly more opportune to integrate these data in the form of a global, selfconsistent, predictive model. Although first heuristic and then mathematical and statistical models have already been proposed (SZENTAGOTHAI, 1963, 1965; MARR, 1969; ALBUS, 1971; MITTENTHAL, 1974), it remains necessary to resort to simulation, using a digital computer, to provide precise predictions on a cellular level for any model of a particular cerebellum. Several efforts along these lines have been published (PELLIONISZ, 1970, 1972; MORTIMER, 1970, 1973; MENO, 1971; CALVERT & MENO, 1972). Our own earlier modeling work (PELLIONISZ & SZENTAGOTHAI, 1973, 1974) was designed to check the quantitative morphological parameters of the system, as measured by PALKOMTS, MAGYAR & SZENTAGOTHAI (1971aJJ; 1972). Abbreviations: CF, climbing fibers; GrC, granule cells; MF, mossy fibers; PC, Purkinje cells; PF, parallel fibers. The modeling efforts indicated a need to obtain specific data absent at that time and pointed out the existence of numerical inconsistencies. But more importantly, these studies suggested that modeling based on pure connectivity had serious limitations. Moreover, these attempts reinforced the suggestion based on single-unit recordings that the individual functional properties of ‘the Purkinje cells are crucial to an understanding of the functioning of the cerebellar cortex (LLINAS, PRECHT & CLARKE, 1971). For these reasons, we based the present simulation model on single neurons, their behavior being characterized by nonlinear features, as opposed to modeling concepts in which the ‘unit’ is an assembly of neurons, often described by linear features. As suggested previously (LLINAs, 1971), the frog cerebellum is best suited for this type of modeling on several grounds: (1) Experimental data are abundant both on the morphology and physiology of the frog cerebellum (HILLMAN, 1969a,b; SCITELO, 1969; LLINAS, BLQEDEL & HILLMAN, 1969 ; FABER & KORN, 1970; RUSHMER, 1970; RUSHMER & WOODWARD, 1971; HACKETT, 1972; FREEMAN & NICHOLSON, 1975). (2) The relatively simple organization, the simplicity of the interneuronal inhibitory systems (HILLMAN, 20 A. PELLIONISZ, R. LLIN.~S and D. H. PERKEL 1969b; SOTELO, 1969) and the relatively small number of neurons (below two million) made it plausible to attempt modeling the entire cerebellar cortex. (3) The well-studied vestibulo-cerebellar system in the frog lends itself to modeling input-output relationships under physiological stimulation (PRECHT • LLINAS, 1969; LLrNAS et al., 1971; LLIN.~S & PRECHT, 1972; MAGHERINI; GIRETH & PRECHT, 1975; BLANKS, GIRETTI & PRECHT, 1975a, b). The paper describes the physiological and anatomical assumptions of the model and illustrates its application to a specific set of experiments: the input-output relations of the cerebellar cortex under physiological stimulation of the vestibular system. METHODS Basic concepts of the model The number of neurons in the frog cerebellar cortex is far too large to permit their representation, in however crude a model, within the core memory of the computer available to us (IBM 360/67 at the Campus Facility of the Stanford Center for Information Processing) and, in fact, precluded a straightforward representation of the network on magnetic disc storage compatible with minimal criteria of economy. A neuron-by-neuron simulation was made possible only by programming the computer to 'grow' or reconstruct those particular neuronal pathways that participate in the specific stimulus-response experiment being simulated. As described below, the assignment of specific parametric values of morphological characteristics is made at random, according to specified probability distributions and other constraints. For brevity, we refer to this aspect of the program as 'morphogenesis', although we have made no attempt to mimic the actual sequence of events in the histological development of the cerebellum. All programs were written in FORTRAN. Those which required extensive core memory were run on an IBM 360/67; those providing visual displays were run on the PDP-15 computer graphics system in our department, which includes a dynamic display with writing tablet and light pen, a storage oscilloscope static display, 32 K of core memory and both disc and tape forms of auxiliary storage. Shape of the frog cerebellum As illustrated in Fig. 1 A and B, the frog cerebellum may be represented as a transversely oriented, threelayered slab, located behind the optic tecta. The body of the cerebellum arches over the fourth ventricle; its lateral extensions, the cerebellar peduncles, provide the entry points for the afferent pathways: mossy fibers (MF) and climbing fibers (CF) and the exit points for the efferent fibers: Purkinje cell (PC) axons. The dimensions are shown in Fig. 1 D. The caudal layer is the granular layer, the place of entry and ramification of the MF system, in which the MFs make synaptic contact with the granule cells (GrC). The axons of the granule cells rise into the rostrally situated molecular layer, where they form T-shaped bifurcations, running transversely and strictly parallel to one another, constituting the parallel fibers (PF). The granular and molecular layers are separated by a sheet of PCs: the Purkinje cell layer. The dendritic trees of the PCs protrude into the molecular layer, within which they are contacted synaptically by the orthogonally oriented PFs. C ~ GrL : 4 0 0 x 1 4 5 x 2 9 = 1.68x106 GrC A ~ ,~ ' i ~ 1.45 pet : 8285 Pc m