Conversion of Electrical and Synaptic Actions into Impulse Discharge Patterns in Purkinje Neurons with Active Dendrites: A Simulation Study

We studied relations between the cell output spiking patterns (neuronal codes) and the intensity of input signals on a model of cerebellar Purkinje neuron with reconstructed dendritic arborization and nonlinear membrane properties. The input influences were either a depolarizing current, I _s, applied at the soma or tonic synaptic excitation resulting in a synaptic conductivity, G _s homogeneously distributed over the dendrites. The spiking patterns were distinguished based on periodical or nonperiodical (stochastic) sequences of spikes and/or their groups (bursts). The role of dendrites in pattern forming was revealed from time-varying spatial distributions of the dendritic membrane potential and the corresponding voltages in the soma and distal axon. As integrative indicators, interspike intervals, ISIs, and mean firing rates, f, characterized the output spiking, while mean voltage differences, ΔĒ, between the remotest equidistant sites in all pairs of the sister dendrite branches characterized the electrical heterogeneity of the arborization. To explore a wide range of conditions, I _st and G _s were varied, respectively, from 0.55 to 1.4 nA and from 50 μS/cm² to 7 mS/cm² On average, the output firing rate f increased with increased intensities of either input signal. The f-I _st and f-G _s relations, however, differed from each other. The former was an approximately logarithmic function with small deviations at mid-range currents, while the latter was a nonmonotonically increasing function with remarkable slope breaks within an intermediate Gs range. Within the intensity ranges, the electrical heterogeneity of the arborization ΔĒ increased with greater I _st, but it first increased and then decreased with increasing G _s. The leading pattern-forming factor of dendritic origin consists of transitions of the dendritic domains between states of spatially homogeneous near-resting depolarization (down-state) and spatially heterogeneous high depolarization (up-state) manifested as the appearance of slow plateau-like depolarization potentials. The latter were generated with phase shifts between dendritic subtrees in response to the applied current I _st > 1.5 nA (about threefold greater than the threshold current) or in response to synaptic activation of low (G _s ≤ 66 μS/cm²) and high (G _s > 75 μS/cm²), but not intermediate intensities. Under these conditions, the output patterns were either continuous firing with nearly constant ISIs or simple periodical sequences of identical bursts accompanied by moderate elevations of ΔĒ. At intermediate synaptic intensities, the synchronous transitions were periodically perturbed by nonsynchronous ones, leading to generation of several dissimilar bursts or “single spike-burst” complexes. These events were associated with the largest ΔĒ elevations indicating the greatest electrical heterogeneity of the arborization. Such desynchronized transitions are explained by the existence of an asymmetry-induced difference in the transfer properties of the dendrite subtrees, leading to increased differences in the electrical states. We conclude that the dendritic arborization of Purkinje neurons behaves like a complex of high-threshold low-frequency spatial electrical oscillators, while the axo-somatic trigger zone has a low threshold and is capable of providing a high firing frequency. These properties determine the conversion of the input signal intensity into output firing patterns depending on which of these coupled oscillators is at present the predominant receiver of the input signal and also on the input intensity.