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The spatiotemporal stochastic dynamics of the voltage as well as theupcrossing rate are derived for a model neuron comprising a long dendrite withuniformly distributed filtered excitatory and inhibitory synaptic drive. Acascade of ordinary and partial differential equations is obtained describingthe evolution of first-order means and second-order spatial covariances of thevoltage and its rate of change. These quantities provide an analytical form forthe general, steady-state and linear response of the upcrossing rate to dynamicsynaptic input. It is demonstrated that this minimal dendritic model has anunexpectedly sustained high-frequency response despite synaptic, membrane andspatial filtering.

Upcrossing-rate dynamics for a minimal neuron model receiving spatially distributed synaptic drive