Interpretation of neuronal response properties with simplified neuron models

Computational neuroscience is a branch of the neurosciences that attempts to elucidate the principles underlying the operation of neurons with the help of mathematical modeling. In contrast with a number of fields pursuing a tightly related goal, such as machine learning or statistical learning, computational neuroscience emphasizes the realistic description of neuronal function and organization, and therefore requires a collaboration with experimental research in order to design new models and test their predictions. With the growing computational power available in modern computers, the simulation of neuronal networks with realistic numbers of neurons and functional organization is becoming routinely accessible. For the accurate design of such network models, the experimental characterization of neuronal response properties is required to probe the structural layout of biological networks at the single cell level. We develop here a novel method, the dynamic I-V method, that allows for the extraction of cellular response properties, and requires only a small amount of experimental data. Using this technique a simplified model of the neuronal response is obtained that is shown to accurately fit the experimental data. We demonstrate the use of the dynamic I-V method on both cortical pyramidal cells and inhibitory interneurons, and give the distributions of cellular parameters for the studied sample of cells. We also give theoretical results on the spike-triggered average, a quantity that is easily measured experimentally, which relate the neuronal response properties to identifiable features of the spike-triggered average, and can potentially be helpful to extend the dynamic I-V method in order to derive more accurate models. Potential applications and extensions of our results are discussed.