The present paper explores the possible functional significance of the parallel orientation of parallel fibers in teleostean cerebellar and cerebelloid molecular layers, taking advantage of the restricted width of these molecular layers compared with mammalian ones and several specific configurations of granule cells. These configurations include: (i) a unilateral location, i.e. at only one (lateral) side of the molecular layer, giving rise to parallel fibers without bifurcation in a unidirectional molecular layer, where all parallel fibers conduct signals in the same direction; (ii) a bilateral location at both sides of the molecular layer giving rise to a bidirectional molecular layer where parallel fibers conduct signals in two opposite directions originating from two discrete sources; and (iii) a basal (or sometimes apical) location underneath (or opposite to) the layer of Purkinje cells, giving rise to a bidirectional molecular layer where parallel fibers conduct signals in two opposite directions originating from a continuous range of sources. It is argued that molecular layers with a bilateral location of granule cells, exemplified by the mormyrid lobus transitorius, represent an optimal configuration for the analysis of small temporal differences (up to 4 ms) between inputs to the right and left granule cell mass, by means of detection of the site of coincidence of parallel fiber activity running from left to right and vice versa. Morphological aspects that probably optimize such a function include not only the parallel course and bilateral origin of parallel fibers, but also their small diameter, large number and co-extensive location, as well as the sagittal orientation and the presence of many spines of Purkinje cell dendrites and the presence of stellate and other inhibitory interneurons. The only assumption underlying the present coincidence detection hypothesis is that Purkinje cells are supposed to be maximally stimulated by parallel fiber input when all spines are activated in such a way that their excitatory postsynaptic potentials reach the axon hillock simultaneously. For molecular layers with a unilateral location of granule cells, exemplified by the teleostean torus longitudinalis-tectal marginal parallel fiber system, a similar coincidence detecting mechanism is proposed on the basis of the presence of two populations of parallel fibers with slightly different conduction velocities. Such a system might be suitable to adapt the location of coincidence peaks to topographic maps present in deeper layers of nervous tissue. Molecular layers with basally (or apically) located granule cells as encountered in the teleostean corpus cerebelli, are probably involved in the analysis of specific spatio-temporal input waves directed centripetally towards different Purkinje cells. Compared with monoor bilateral locations of granule cells, a basal location of granule cells adds specificity at the expense of sensitivity to the coincidence detecting properties of the molecular layer, and requires a more precise topographic organization of mossy fiber input. The possible functional significance of the configurations analysed is discussed on the basis of the literature available, while their specific advantages and constraints are evaluated using a model of the teleostean lateral line system. This system presents a nice example of different configurations of similar sensors at the same sensory interface working within the same space-time domain. Comparison of the teleostean cerebellar configurations analysed with the mammalian one suggests that the dramatically larger width of the latter does not only allow for the detection of a larger range of temporal differences and spatiotemporal input wave patterns, but might also reduce artefacts by juxtaposition of distinct zones with a similar input. The presence of basket cells and the discongruent extension of parallel fibers in the mammalian cerebellum might also optimize coincidence detection. Comparison with the acoustic and electrosensory communication system, where similar coincidence detection mechanisms have been demonstrated, suggests that these subserve fast analysis of phase differences of relatively simple, repetitive input of high frequency (an acoustic or electric tone), whereas cerebellar coincidence detection is probably involved in slower analysis of temporal differences of single or low-frequency repetitive inputs with a more complex and noisy shape and pattern. Finally, it is suggested that the specific palisade orientation of the dendrites of mormyrid Purkinje cells might well increase the tuning of Purkinje cells for specific input waves, not only in the transverse direction, but also in the apico-basal and rostro-caudal direction, and thus probably represents an ultimate optimization for cerebellar coincidence detection. In contrast, the mammalian Purkinje cell configuration seems optimal for integration of parallel fiber input with climbing fiber input, possibly involved in gain control of coincidence detection.
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