Network analysis of dendritic fields of pyramidal cells in neocortex and Purkinje cells in the cerebellum of the rat

Abstract

The connectivity within the dendritic array of Purkinje cells in the cerebellum and pyramidal cells of the neocortex of the rat, stained by the Golgi-Cox method, has been quantified by the method of network analysis. Connectivity was characterized either by applying die system of Strahler ordering, which assigns a relative order of magnitude to each branch of the arborescence or by the identification of unique topological branching patterns within the tree. The former method has been used to define the entire dendritic array of the Purkinje cell and the apical system of neocortical pyramids It has been shown that the relation between the numbers of branches of successive Strahler order in Purkinje cells form an inverse geometric series in which the highest order is unity and the ratio between successive orders approximates to 3. On the other hand, the apical dendrites of neocortical pyramids exhibit two bifurcation ratios, i.e. a ratio of 3 between low orders and a ratio of 4 between higher orders. A computer simulation technique was used to generate networks of a size comparable with the Purkinje cell networks and grown according to two hypotheses namely, a ‘terminal growth model’ in which additional segments were added randomly to the terminal branches only and a ‘segmental growth model’ in which additional segments were added randomly to any branch within the array including terminal branches. Subsequent ordering of the simulated trees revealed that the relation between the numbers of successive orders for networks generated according to the ‘segmental model' tended towards an inverse geometric series with a ratio of 4 and that generated according to the ‘terminal model’ tended towards a ratio of 3. This result showed that the dendritic tree of Purkinje cells grow in a manner indistinguishable from a system adding branches to random terminal segments and that neocortical apical dendrites add their collateral branches to random segments of the apical shaft but that the collateral branches themselves grow by random terminal branching. The possibility that such conclusions may be influenced by loss of branches incurred by either a failure of impregnation, by sectioning, or by environmental influences was investigated by means of a computer technique. It was shown that providing such losses occur randomly there is no significant disturbance between the relative number of successive orders. The method of ordering used gives more precise information about connectivity if the branches are further divided into segments by noting the order of branches converging at each node. It has been shown that the majority of the dendrites of the Purkinje cells are organized into systems of fourth order or less which merge with relatively few fifth, sixth and seventh order branches. These differences in the two parts of the tree were further reflected by equivalent differences in the lengths of branches in the two parts of the tree. The analysis of unique topological branching patterns was used to study the growth of both the basal dendrites of neocortical pyramids, the side branches of apical dendrites, and the dendrites of Purkinje cells. The frequency distribution of distinct topological branching patterns were enumerated for networks with from 4-7 terminal branches and compared with those expected from networks grown according to the ‘terminal’ and ‘segmental’ growth models. In every case the analysis showed good agreement with the terminal model and no agreement with the alternative hypothesis, strongly suggesting that these dendritic systems of both cells grow by branching randomly on terminal segments. With a complete series of topological types of branching patterns for networks with a given number of terminal branches, generated according to either hypothesis, ‘ absolute bifurcation ratios ’ may be computed between each order by applying the same method of ordering that was used for the dendrites in Purkinje cells. The absolute bifurcation ratios of networks with a given number of terminal branches are defined as the ratios between adjacent orders in a complete series of topological types. This latter parameter was also used to test the above hypotheses of growth in the small networks of the basal dendrites of neocortical pyramids and substantiated the findings that the topology of these dendrites is established by branching randomly on terminal segments only. The above results are discussed in relation to the basic principle of network analysis, nature-nurture influences on the growth of dendritic fields and the implications of differing branching patterns on the neurophysiology of the dendritic system.