Cerebellar Purkinje cells display complex intrinsic dynamics. They fire spontaneously, exhibit bistability, and via mutual network interactions are involved in the generation of high frequency oscillations and travelling waves of activity. To probe the dynamical properties of Purkinje cells we measured their phase response curves (PRCs). PRCs quantify the change in spike phase caused by a stimulus as a function of its temporal position within the interspike interval, and are widely used to predict neuronal responses to more complex stimulus patterns. Significant variability in the interspike interval during spontaneous firing can lead to PRCs with a low signal-to-noise ratio, requiring averaging over thousands of trials. We show using electrophysiological experiments and simulations that the PRC calculated in the traditional way by sampling the interspike interval with brief current pulses is biased. We introduce a corrected approach for calculating PRCs which eliminates this bias. Using our new approach, we show that Purkinje cell PRCs change qualitatively depending on the firing frequency of the cell. At high firing rates, Purkinje cells exhibit single-peaked, or monophasic PRCs. Surprisingly, at low firing rates, Purkinje cell PRCs are largely independent of phase, resembling PRCs of ideal non-leaky integrate-and-fire neurons. These results indicate that Purkinje cells can act as perfect integrators at low firing rates, and that the integration mode of Purkinje cells depends on their firing rate.

Simultaneous recordings from multiple neural units allow us to investigate the activity of very large neural ensembles. To understand how large ensembles of neurons process sensory information, it is necessary to develop suitable statistical models to describe the response variability of the recorded spike trains. Using the information geometry framework, it is possible to estimate higher-order correlations by assigning one interaction parameter to each degree of correlation, leading to a (2 N − 1)-dimensional model for a population with N neurons. However, this model suffers greatly from a combinatorial explosion, and the number of parameters to be estimated from the available sample size constitutes the main intractability reason of this approach. To quantify the extent of higher than pairwise spike correlations in pools of multiunit activity, we use an information-geometric approach within the framework of the extended central limit theorem considering all possible contributions from high-order spike correlations. The identification of a deformation parameter allows us to provide a statistical characterisation of the amount of high-order correlations in the case of a very large neural ensemble, significantly reducing the number of parameters, avoiding the sampling problem, and inferring the underlying dynamical properties of the network within pools of multiunit neural activity.

While the neuronal activity of the cerebral cortex is strongly modulated by sensory inputs, the cortex also exhibits rich spontaneous dynamics. Experimental evidence suggests that sensory stimulation may shape the spontaneous activity of the cortex, which in turn can influence its responses to further external stimulation. However, we still do not understand how sensory stimuli affect the underlying neural circuitry. Here we study whether spike-timing-dependent plasticity (STDP) can mediate sensory-induced modifications in the spontaneous dynamics of a new large-scale model of layers II, III and IV of the rodent barrel cortex. A central feature of our model is its level of physiological detail, including the types of neurons present, the probabilities and delays of connections, and the STDP profiles at each excitatory synapse. We stimulated the neuronal network with a protocol of repeated sensory inputs, resembling those generated by the protraction-retraction motion of whiskers when rodents explore their environment, and studied the changes in network dynamics. By applying dimensionality reduction techniques to the synaptic weight space, we show that the trajectories converge to an initial spontaneous attractor state, which is modified by each repetition of the stimulus. This reverberation of the sensory experience induces long-term modifications in the synaptic weight space. The post-stimulus spontaneous state encodes a unique memory of the stimulus presented, since a different dynamical response is observed when the network is presented with shuffled stim- uli. These results suggest that repeated exposure to the same sensory experience could induce long-term circuitry modifications via 'Hebbian' STDP plasticity.

Author contributions: E.P., M.B. and S.R.S. jointly conceived the study and designed the experiments. E.P. performed the electrophysiological recordings, collected and analyzed the data. A.B. performed the histological and imaging procedures. E.P., M.B. and S.R.S. wrote the manuscript. Keywords Barrel cortex, plasticity, spontaneous activity, electrophysiology 20 pages, 6 figures 2 Neocortical circuits exhibit spontaneous neuronal activity whose functional relevance remains enigmatic. Several proposed functions assume that sensory experience can influence subsequent spontaneous activity. However, long-term alterations in spontaneous firing rates following sensory stimulation have not been reported until now. Here we show that multi-whisker, spatiotemporally rich stimulation of mouse vibrissae induces a laminar-specific, long-term increase of spontaneous activity in the somatosensory cortex. Such stimulation additionally produces stereotypical neural ensemble firing patterns from simultaneously recorded single neurons, which are maintained during spontaneous activity following stimulus offset. The increased neural activity and concomitant ensemble firing patterns are sustained for at least 25 minutes after stimulation, and specific to layers IV and Vb. In contrast, the same stimulation protocol applied to a single whisker fails to elicit this effect. Since layer Vb has the largest receptive fields and, together with layer IV, receives direct thalamic and lateral drive, the increase in firing activity could be the result of mechanisms involving the integration of spatiotemporal patterns across multiple whiskers. Our results provide direct evidence of modification of spontaneous cortical activity by sensory stimulation and could offer insight into the role of spatiotemporal integration in memory storage mechanisms for complex stimuli. Arabzadeh E, Zorzin E, Diamond ME (2005) Neuronal encoding of texture in the whisker sensory pathway. PLoS Biol 3:e17. Arieli A, Sterkin A, Grinvald A, Aersten A (1996) Dynamics of ongoing activity: explanation of the large variability in evoked cortical responses. Science 273:1868-1871. Azouz R, Gray C (1999) Cellular mechanism contributing to response variability of cortical neurons in vivo. J Neurosci 19:2209-2223. Blanche TJ, Spacek MA, Hetke JF, Swindale NV (2005) Polytrodes: high-density silicon electrode arrays for large-scale multiunit recording. J Neurophysiol 93:2987-3000. Boucsein C, Nawrot MP, Schnepel P, Aersten A (2011) Beyond the cortical column: abundance and physiology of horizontal connections imply a strong role for inputs from the surround. Front 16 Neurosci 5:1-13. Brecht M, Grinevich V, Jin TE, Margrie T, Osten P (2006) Cellular mechanisms of motor control in the vibrissal system. Pflügers Arch. -Eur. J. Physiol. 453:269-281. Bruno RM, Simons DJ (2002) Feedforward mechanisms of excitatory and inhibitory receptive fields. J Neurosci 22:10966-10975. Chagnac-Amitai Y, Connors BW (1989) Synchronized excitation and inhibition driven by intrinsically bursting neurons in...