Neural signaling requires a large amount of metabolic energy 1 . Consequently, neurons are thought to communicate using efficient codes in which redundant information is discarded 2 . Theories of efficient coding 3 successfully predict several features of sensory systems. At early stages of visual processing, inputs coming from the external world are decorrelated in both space and time [4][5][6][7] ; through sensory adaptation 8 , codes are dynamically modified so as to maximize information transmission [9][10][11][12] ; and sensory adaptation on multiple timescales 11,13,14 could possibly reflect the statistics of the external world 15 .Sensory adaptation is at least partially a result of intrinsic properties of individual neurons and, in particular, of SFA. SFA is not only observed at the early stages of sensory processing, but is also widespread in cortical neurons embedded in highly recurrent networks. Often modeled by a single process with one specific timescale 16,17 , SFA also occurs on multiple timescales [18][19][20] . In pyramidal neurons of the rat somatosensory cortex, three or more processing steps away from sensory receptors, SFA is scale free 21 , meaning that the effective speed at which individual neurons adapt is not fixed but depends on the input. Scale-free adaptation can be captured by simple threshold models with a power law-decaying spike-triggered process 22 that possibly describes the combined action of Na + -channel inactivation [23][24][25] and ion channels mediating adaptation currents [26][27][28] .Thus, three questions arise. First, can the temporal features of spiketriggered currents and spike-triggered changes in firing threshold, possibly spanning multiple timescales, be directly extracted from experimental data? Second, can SFA be explained by these spiketriggered effects? And finally, do the timescales of SFA match the temporal statistics of the inputs received by individual neurons? If temporal characteristics of inputs and SFA were matched, SFA could lead to a perfect decorrelation of the information contained in one spike with that of the previous one of the same neuron, a phenomenon known as temporal whitening 29 . Temporal whitening in turn implies that, at a high signal-to-noise ratio (SNR), information transmission is enhanced 30 . RESULTSThe question of whether SFA is optimally designed for efficient coding can only be addressed if both the dynamics of SFA and the statistical properties of the inputs generated in biologically relevant situations are known. We used a combined theoretical and experimental approach to extract the dynamics of spike-triggered processes and SFA directly from in vitro recordings of cortical neurons. We then analyzed the synaptically driven membrane potential dynamics recorded in vivo from somatosensory neurons during active whisker sensation (data from ref. 31). Our overall goal was to study whether adaptation optimally removes the temporal correlations in the input to single neurons embedded in the highly recurrent network of the cortex.SFA i...

Cortical information processing originates from the exchange of action potentials between many cell types. To capture the essence of these interactions, it is of critical importance to build mathematical models that reflect the characteristic features of spike generation in individual neurons. We propose a framework to automatically extract such features from current-clamp experiments, in particular the passive properties of a neuron (i.e., membrane time constant, reversal potential, and capacitance), the spike-triggered adaptation currents, as well as the dynamics of the action potential threshold. The stochastic model that results from our maximum likelihood approach accurately predicts the spike times, the subthreshold voltage, the firing patterns, and the type of frequency-current curve. Extracting the model parameters for three cortical cell types revealed that cell types show highly significant differences in the time course of the spike-triggered currents and moving threshold, that is, in their adaptation and refractory properties but not in their passive properties. In particular, GABAergic fast-spiking neurons mediate weak adaptation through spike-triggered currents only, whereas regular spiking excitatory neurons mediate adaptation with both moving threshold and spike-triggered currents. GABAergic nonfast-spiking neurons combine the two distinct adaptation mechanisms with reduced strength. Differences between cell types are large enough to enable automatic classification of neurons into three different classes. Parameter extraction is performed for individual neurons so that we find not only the mean parameter values for each neuron type but also the spread of parameters within a group of neurons, which will be useful for future large-scale computer simulations.

Single-neuron models are useful not only for studying the emergent properties of neural circuits in large-scale simulations, but also for extracting and summarizing in a principled way the information contained in electrophysiological recordings. Here we demonstrate that, using a convex optimization procedure we previously introduced, a Generalized Integrate-and-Fire model can be accurately fitted with a limited amount of data. The model is capable of predicting both the spiking activity and the subthreshold dynamics of different cell types, and can be used for online characterization of neuronal properties. A protocol is proposed that, combined with emergent technologies for automatic patch-clamp recordings, permits automated, in vitro high-throughput characterization of single neurons.

The way in which single neurons transform input into output spike trains has fundamental consequences for network coding. Theories and modeling studies based on standard Integrate-and-Fire models implicitly assume that, in response to increasingly strong inputs, neurons modify their coding strategy by progressively reducing their selective sensitivity to rapid input fluctuations. Combining mathematical modeling with in vitro experiments, we demonstrate that, in L5 pyramidal neurons, the firing threshold dynamics adaptively adjust the effective timescale of somatic integration in order to preserve sensitivity to rapid signals over a broad range of input statistics. For that, a new Generalized Integrate-and-Fire model featuring nonlinear firing threshold dynamics and conductance-based adaptation is introduced that outperforms state-of-the-art neuron models in predicting the spiking activity of neurons responding to a variety of in vivo-like fluctuating currents. Our model allows for efficient parameter extraction and can be analytically mapped to a Generalized Linear Model in which both the input filter—describing somatic integration—and the spike-history filter—accounting for spike-frequency adaptation—dynamically adapt to the input statistics, as experimentally observed. Overall, our results provide new insights on the computational role of different biophysical processes known to underlie adaptive coding in single neurons and support previous theoretical findings indicating that the nonlinear dynamics of the firing threshold due to Na+-channel inactivation regulate the sensitivity to rapid input fluctuations.

Multiple measures have been developed to quantify the similarity between two spike trains. These measures have been used for the quantification of the mismatch between neuron models and experiments as well as for the classification of neuronal responses in neuroprosthetic devices and electrophysiological experiments. Frequently only a few spike trains are available in each class. We derive analytical expressions for the small-sample bias present when comparing estimators of the time-dependent firing intensity. We then exploit analogies between the comparison of firing intensities and previously used spike train metrics and show that improved spike train measures can be successfully used for fitting neuron models to experimental data, for comparisons of spike trains, and classification of spike train data. In classification tasks, the improved similarity measures can increase the recovered information. We demonstrate that when similarity measures are used for fitting mathematical models, all previous methods systematically underestimate the noise. Finally, we show a striking implication of this deterministic bias by reevaluating the results of the single-neuron prediction challenge.