Statistical analysis and parsimonious modelling of dendrograms of in vitroneurones

The processes whereby developing neurones acquire morphological features th at are common to entire populations (thereby allowing the definition of neu ronal types) are still poorly understood. A mathematical model of neuronal arborizations may be useful to extract basic parameters or organization rul es, hence helping to achieve a better understanding of the underlying growt h processes. We present a parsimonious statistical model, intended to describe the topol ogical organization of neuritic arborizations with a minimal number of para meters. It is based on a probability of splitting which depends only on the centrifugal order of segments. We compare the predictions made by the mode l of several topological properties of neurones with the corresponding actu al values measured on a sample of honeybee (olfactory) antennal lobe neuron es grown in primary culture, described in a previous study. The comparison is performed for three populations of segments corresponding to three neuro nal morphological types previously identified and described in this sample. We show that simple assumptions together with the knowledge of a very smal l number of parameters allow the topological reconstruction of representati ve (bi-dimensional) biological neurones. We discuss the biological signific ance tin terms of possible factors involved in the determinism of neuronal types) of both common properties and cell-type specific features, observed on the neurones and predicted by the model. (C) 2000 Society for Mathematic al Biology.