Bridging neuronal correlations and dimensionality reduction

Two commonly used approaches to study interactions among neurons are spike count correlation, which describes pairs of neurons, and dimensionality reduction, applied to a population of neurons. Although both approaches have been used to study trial-to-trial neuronal variability correlated among neurons, they are often used in isolation and have not been directly related. We first established concrete mathematical and empirical relationships between pairwise correlation and metrics of population-wide covariability based on dimensionality reduction. Applying these insights to macaque V4 population recordings, we found that the previously reported decrease in mean pairwise correlation associated with attention stemmed from three distinct changes in population-wide covariability. Overall, our work builds the intuition and formalism to bridge between pairwise correlation and population-wide covariability and presents a cautionary tale about the inferences one can make about population activity by using a single statistic, whether it be mean pairwise correlation or dimensionality.

Tuning of Neuronal Interactions in the Lateral Ventral Tegmental Area by Dopamine Sensitivity

The Ventral Tegmental Area (VTA) contains a considerable population of rhythmically firing dopaminergic neurons, which are influenced by auto-inhibition due to extra-synaptic dopamine release resulting in volume transmission. Using a Multi-Electrode-Array we simultaneously recorded in vitro from multiple VTA dopamine neurons in the rat and studied their mutual interactions. We observed that the dopamine sensitivity (EC50) of the neurons (i.e. the relation between dopamine concentration and firing rate) was quite variable within the recorded population. The interactions between pairs of neurons were quantified using the Granger causality. We found that the dopamine sensitivity determined the role of a neuron in the local VTA population. Highly sensitive neurons became followers (of the population rhythm), whereas less sensitive dopamine neurons played a more leading role. This was confirmed by the application of sulpiride which reduces the dopamine sensitivity of all neurons through competition and abolishes the structure in the interactions. These findings imply that therapeutics, which have an easy to understand effect on firing rate, could have a more complicated effect on the functional organization of the local VTA population, through volume transmission principles.

Firing Properties of Genetically Identified Dorsal Raphe Serotonergic Neurons in Brain Slices

Tonic spiking of serotonergic neurons establishes serotonin levels in the brain. Since the first observations, slow regular spiking has been considered as a defining feature of serotonergic neurons. Recent studies, however, have revealed the heterogeneity of serotonergic neurons at multiple levels, comprising their electrophysiological properties, suggesting the existence of functionally distinct cellular subpopulations. In order to examine in an unbiased manner whether serotonergic neurons of the dorsal raphe nucleus (DRN) are heterogeneous, we used a non-invasive loose-seal cell-attached method to record α1 adrenergic receptor-stimulated spiking of a large sample of neurons in brain slices obtained from transgenic mice lines that express fluorescent marker proteins under the control of serotonergic system-specific Tph2 and Pet-1 promoters. We found wide homogeneous distribution of firing rates, well fitted by a single Gaussian function (r (2) = 0.93) and independent of anatomical location (P = 0.45), suggesting that in terms of intrinsic firing properties, serotonergic neurons in the DRN represent a single cellular population. Characterization of the population in terms of spiking regularity was hindered by its dependence on the firing rate. For instance, the coefficient of variation of the interspike intervals (ISI), a common measure of spiking irregularity, is of limited usefulness since it correlates negatively with the firing rate (r = -0.33, P < 0.0001). Nevertheless, the majority of neurons exhibited regular, pacemaker-like activity, with coefficient of variance of the ISI lower than 0.5 in ~97% of cases. Unexpectedly, a small percentage of neurons (~1%) exhibited a particular spiking pattern, characterized by low frequency (~0.02-0.1 Hz) oscillations in the firing rate. Transitions between regular and oscillatory firing were observed, suggesting that the oscillatory firing is an alternative firing pattern of serotonergic neurons.

Population dynamics of the modified theta model: macroscopic phase reduction and bifurcation analysis link microscopic neuronal interactions to macroscopic gamma oscillation

Gamma oscillations of the local field potential are organized by collective dynamics of numerous neurons and have many functional roles in cognition and/or attention. To mathematically and physiologically analyse relationships between individual inhibitory neurons and macroscopic oscillations, we derive a modification of the theta model, which possesses voltage-dependent dynamics with appropriate synaptic interactions. Bifurcation analysis of the corresponding Fokker-Planck equation (FPE) enables us to consider how synaptic interactions organize collective oscillations. We also develop the adjoint method (infinitesimal phase resetting curve) for simultaneous equations consisting of ordinary differential equations representing synaptic dynamics and a partial differential equation for determining the probability distribution of the membrane potential. This method provides a macroscopic phase response function (PRF), which gives insights into how it is modulated by external perturbation or internal changes of parameters. We investigate the effects of synaptic time constants and shunting inhibition on these gamma oscillations. The sensitivity of rising and decaying time constants is analysed in the oscillatory parameter regions; we find that these sensitivities are not largely dependent on rate of synaptic coupling but, rather, on current and noise intensity. Analyses of shunting inhibition reveal that it can affect both promotion and elimination of gamma oscillations. When the macroscopic oscillation is far from the bifurcation, shunting promotes the gamma oscillations and the PRF becomes flatter as the reversal potential of the synapse increases, indicating the insensitivity of gamma oscillations to perturbations. By contrast, when the macroscopic oscillation is near the bifurcation, shunting eliminates gamma oscillations and a stable firing state appears. More interestingly, under appropriate balance of parameters, two branches of bifurcation are found in our analysis of the FPE. In this case, shunting inhibition can effect both promotion and elimination of the gamma oscillation depending only on the reversal potential.

Electrophysiological characterization of entopeduncular nucleus neurons in anesthetized and freely moving rats

The EntoPeduncular nucleus (EP), which is homologous to the internal segment of the Globus Pallidus (GPi) in primates, is one of the two basal ganglia (BG) output nuclei. Despite their importance in cortico-BG information processing, EP neurons have rarely been investigated in rats and there is no available electrophysiological characterization of EP neurons in vivo. We recorded and analyzed the activity of EP neurons in freely moving as well as anesthetized rats, and compared their activity patterns. Examination of neuronal firing statistics during wakefulness suggested that similar to neurons recorded in the primate GPi, EP neurons are a single population characterized by Poisson-like firing. Under isoflurane anesthesia the firing rate of EP neurons decreased substantially and their coefficient of variation and relative duration of quiescence periods increased. Investigation of the relationship between firing rate and depth of anesthesia revealed two distinct neuronal groups: one that decreased its firing rate with the increase in anesthesia level, and a second group where the firing rate was independent of anesthesia level. Post-hoc examination of the firing properties of the two groups showed that they were statistically distinct. These results may thus help reconcile in vitro studies in rats and primates which have reported two distinct neuronal populations, and in vivo studies in behaving primates indicating one homogeneous population. Our data support the existence of two distinct neuronal populations in the rat EP that can be distinguished by their characteristic firing response to anesthesia.

On the estimation of population-specific synaptic currents from laminar multielectrode recordings

Multielectrode array recordings of extracellular electrical field potentials along the depth axis of the cerebral cortex are gaining popularity as an approach for investigating the activity of cortical neuronal circuits. The low-frequency band of extracellular potential, i.e., the local field potential (LFP), is assumed to reflect synaptic activity and can be used to extract the laminar current source density (CSD) profile. However, physiological interpretation of the CSD profile is uncertain because it does not disambiguate synaptic inputs from passive return currents and does not identify population-specific contributions to the signal. These limitations prevent interpretation of the CSD in terms of synaptic functional connectivity in the columnar microcircuit. Here we present a novel anatomically informed model for decomposing the LFP signal into population-specific contributions and for estimating the corresponding activated synaptic projections. This involves a linear forward model, which predicts the population-specific laminar LFP in response to synaptic inputs applied at different positions along each population and a linear inverse model, which reconstructs laminar profiles of synaptic inputs from laminar LFP data based on the forward model. Assuming spatially smooth synaptic inputs within individual populations, the model decomposes the columnar LFP into population-specific contributions and estimates the corresponding laminar profiles of synaptic input as a function of time. It should be noted that constant synaptic currents at all positions along a neuronal population cannot be reconstructed, as this does not result in a change in extracellular potential. However, constraining the solution using a priori knowledge of the spatial distribution of synaptic connectivity provides the further advantage of estimating the strength of active synaptic projections from the columnar LFP profile thus fully specifying synaptic inputs.