Running head: Efficient estimation of detailed single-neuron models

Reduced models of neuronal activity such as Integrate-and-Fire models allow a description of neuronal dynamics in simple, intuitive terms and are easy to simulate numerically. We present a method to fit an Integrateand -Fire-type model of neuronal activity, namely a modified version of the Spike Response Model, to a detailed Hodgkin-Huxley-type neuron model driven by stochastic spike arrival. In the Hogkin-Huxley model, spike arrival at the synapse is modeled by a change of synaptic conductance. For such conductance spike input, more than 70% of the postsynaptic action potentials can be predicted with the correct timing by the Integrate-andFire -type model. The modified Spike Response Model is based upon a linearized theory of conductance-driven Integrate-and-Fire neuron. Keywords: conductance injection - Integrate-and-Fire model - stochastic input - mapping techniques - predictive power. PACS: 87.10.+e - 87.19.La - 87.17.Nn - 87.17.Aa. 1

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MJ. Dynamic I-V curves are reliable predictors of naturalistic pyramidal-neuron voltage traces. J Neurophysiol 99: 656–666, 2008. First published December 5, 2007; doi:10.1152/jn.01107.2007. Neuronal response properties are typically probed by intracellular measurements of current-voltage (I-V) relationships during application of current or voltage steps. Here we demonstrate the measurement of a novel I-V curve measured while the neuron exhibits a fluctuating voltage and emits spikes. This dynamic I-V curve requires only a few tens of seconds of experimental time and so lends itself readily to the rapid classification of cell type, quantification of heterogeneities in cell populations, and generation of reduced analytical models. We apply this technique to layer-5 pyramidal cells and show that their dynamic I-V curve comprises linear and exponential components, providing experimental evidence for a recently proposed theoretical model. The approach also allows us to determine the change of neuronal response properties after a spike, millisecond by millisecond, so that postspike refractoriness of pyramidal cells can be quantified. Observations of I-V curves during and in absence of refractoriness are cast into a model that is used to predict both the subthreshold response and spiking activity of the neuron to novel stimuli. The predictions of the resulting model are in excellent agreement with experimental data and close to the intrinsic neuronal reproducibility to repeated stimuli.

The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductancebased synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.

Smoothing biophysical data 1

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scales of temporal response in pyramidal and fast spiking cortical neurons. J Neurophysiol 96: 3448–3464, 2006. First published June 28, 2006; doi:10.1152/jn.00453.2006. Neural dynamic processes correlated over several time scales are found in vivo, in stimulus-evoked as well as spontaneous activity, and are thought to affect the way sensory stimulation is processed. Despite their potential computational consequences, a systematic description of the presence of multiple time scales in single cortical neurons is lacking. In this study, we injected fast spiking and pyramidal (PYR) neurons in vitro with long-lasting episodes of step-like and noisy, in-vivo-like current. Several processes shaped the time course of the instantaneous spike frequency, which could be reduced to a small number (1–4) of phenomenological mechanisms, either reducing (adapting) or increasing (facilitating) the neuron’s firing rate over time. The different adaptation/facilitation processes cover a wide range of time scales, ranging from initial adaptation (�10 ms, PYR neurons only), to fast adaptation (�300 ms), early facilitation (0.5–1 s, PYR only), and slow (or late) adaptation (order of seconds). These processes are characterized by broad distributions of their magnitudes and time constants across cells, showing that multiple time scales are at play in cortical neurons, even in response to stationary stimuli and in the presence of input fluctuations. These processes might be part of a cascade of processes responsible for the power-law behavior of adaptation observed in several preparations, and may have far-reaching computational consequences that have been recently described.

The most likely voltage path and large deviations approximations

notes. Statistical analysis of neural data: State-space models and applications to optimal voltage smoothing, tracking nonstationarities, and recursive decoding ∗