Statistical modelling of higher-order correlations in pools of neural activity

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 higher-order spike correlations. The identification of a deformation parameter allows us to provide a statistical characterisation of the amount of higher-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.Instituto de Física de Líquidos y Sistemas BiológicosInstituto de Física La PlataConsejo Nacional de Investigaciones Científicas y Técnica

Statistical modelling of higher-order correlations in pools of neural activity

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 higher-order spike correlations. The identification of a deformation parameter allows us to provide a statistical characterisation of the amount of higher-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.Instituto de Física de Líquidos y Sistemas BiológicosInstituto de Física La PlataConsejo Nacional de Investigaciones Científicas y Técnica

A New Approach for Determining Phase Response Curves Reveals that Purkinje Cells Can Act as Perfect Integrators

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

Sensory induced long-lasting modification of spontaneous activity in the somatosensory cortex: electrophysiological and modelling studies

Emerging evidence suggests that spontaneous neocortical activity is not merely noise but can be modulated and/or engaged by sensory stimulation. We examined whether naturalistic sensory stimulation can induce specific long-term changes in spontaneous cortical state dynamics in the mouse somatosensory cortex, using both in vivo electrophysiology and modelling. Repetitive, high-frequency multi-whisker stimulation using sandpaper resulted in spontaneous ring rate increase of layer IV and Vb multi-units. The ring rate increase in these layers was sustained for at least 25 minutes following the stimulus. The ring rate increase was accompanied by an increase in layer IV sink amplitude. Increase in spontaneous activity was found also in excitatory single-units in layers IV and Vb. Neither the depth of anaesthesia nor stimulus-induced desynchronization could account for this effect. Finally, we found that elimination of lateral inputs, achieved by trimming away all but the principal whisker, abolished the effect. Single-whisker stimulation resulted in a decrease of activity in layers II/III, IV, Vb and VI, and was accompanied by a decrease in layer IV sink amplitude. In parallel, to study whether Spike-Timing-Dependent-Plasticity (STDP) can explain modifications in spontaneous synaptic dynamics, we developed a biologically inspired large-scale model of rodent barrel layers II, III and IV. Our model consists of approximately 4000 spiking neurons, 1.7 million synapses and 2.2 million dynamical variables. Repetitive sensory stimulation induced long-lasting changes in synaptic weights. The initial state of the network, described by a spontaneous attractor, shifted to a post-stimulus stable state following several repetitions of the same structured stimulation pattern. Furthermore, we found that STDP mediated modifications enabled our network to distinguish between structured and shuffled stimuli. Our experimental and modelling results show that sensory experience induces long-term modification of spontaneous activity in the somatosensory cortex. They suggest that lateral projections and time-dependent plasticity mechanisms play an important role in this process