Nonlinear Dynamic Modeling of Synaptically Driven Single Hippocampal Neuron Intracellular Activity

A high-order nonlinear dynamic model of the input-output properties of single hippocampal CA1 pyramidal neurons was developed based on synaptically driven intracellular activity. The purpose of this study is to construct a model that: 1) can capture the nonlinear dynamics of both subthreshold activities [postsynaptic potentials (PSPs)] and suprathreshold activities (action potentials) in a single formalism; 2) is sufficiently general to be applied to any spike-input and spike-output neurons (point process input and point process output neural systems); and 3) is computationally efficient. The model consisted of three major components: 1) feedforward kernels (up to third order) that transform presynaptic action potentials into PSPs; 2) a constant threshold, above which action potentials are generated; and 3) a feedback kernel (first order) that describes spike-triggered after-potentials. The model was applied to CA1 pyramidal cells, as they were electrically stimulated with broadband Poisson random impulse trains through the Schaffer collaterals. The random impulse trains used here have physiological properties similar to spiking patterns observed in CA3 hippocampal neurons. PSPs and action potentials were recorded from the soma of CA1 pyramidal neurons using whole-cell patch-clamp recording. We evaluated the model performance separately with respect to PSP waveforms and the occurrence of spikes. The average normalized mean square error of PSP prediction is 14.4%. The average spike prediction error rate is 18.8%. In summary, although prediction errors still could be reduced, the model successfully captures the majority of high-order nonlinear dynamics of the single-neuron intracellular activity. The model captures the general biophysical processes with a small set of open parameters that are directly constrained by the intracellular recording, and thus, can be easily applied to any spike-input and spike-output neuron.