Nerve cells with irregular processes: demonstration of anisotropic core geometry of a pyramidal cell.
An analytical, recursive method has been developed to demonstrate the anisotropic electrotonic geometry of nerve cells containing varicose or spiny dendrites. The procedure has been based on the distribution of the core geometry of dendrites into modules which consist of module elements where the physical length is much shorter than the actual space constant. The unambiguous representation of the anisotropic core geometry has been possible by plotting the decomposed geometries separated under the condition of the unidirectional spread of the wave front of dendritic potentials. This decomposition has revealed the bidirectional, "smoothed" core geometries as a function of irregular distribution of varicosities or spines. The shape of decomposed core geometries may change according to the position of the input site. The shaping of core geometry reflects the electrotonic effectiveness of a synaptic site to any arbitrary locations which may lead to considerable savings in computations on synaptic effects. The detailed, computer-reconstructed geometry of the apical dendritic field of the pyramidal cell has been analysed by the proposed method. The frequency-dependence of input impedances has been compared between the original and the transformed core geometries assuming that the current is injected into the soma. The significance of dendritic irregularities in the impedance matching has been studied when the shaping of the core geometry has been induced by laminar inputs. The proposed approach may be useful in comparing the input dependence of the receptive fields of different non-smooth cells. The mismatch of the core geometries induced by the opposite travelling waves from the same anatomical location has also been studied and the possible control of the preferred, direction-sensitive activities will be discussed. The important differences between the compartmental modelings based on the known isotropic treatment of dendrites and the more realistic anisotropic approach will be illustrated.