Valeri A. Makarov

Sorting of neural spikes: When wavelet based methods outperform principal component analysis

Sorting of the extracellularly recorded spikes is a basic prerequisite for analysis of the cooperative neural behavior and neural code. Fundamentally the sorting performance is defined by the quality of discriminative features extracted from spike waveforms. Here we discuss two features extraction approaches: principal component analysis (PCA), and wavelet transform (WT). We show that only when properly tuned to the data, the WT technique may outperform PCA. We present a novel method for extraction of spike features based on a combination of PCA and continuous WT. The method automatically tunes its WT part to the data structure making use of knowledge obtained by PCA. We demonstrate the method on simulated and experimental data sets.

Wavelets in Neuroscience

MathematicalMethods of Signal Processing in Neuroscience.- Brief Tour of Wavelet Theory.- Analysis of Single Neuron Recordings.- Classification of Neuronal Spikes from Extracellular Recordings.- Wavelet Approach to the Study of Rhythmic Neuronal Activity.- Time-Frequency Analysis of EEG: From Theory to Practice.- Automatic Diagnostics and Processing of EEG.- Conclusion.- Index.

A method for determining neural connectivity and inferring the underlying network dynamics using extracellular spike recordings

In the present paper we propose a novel method for the identification and modeling of neural networks using extracellular spike recordings. We create a deterministic model of the effective network, whose dynamic behavior fits experimental data. The network obtained by our method includes explicit mathematical models of each of the spiking neurons and a description of the effective connectivity between them. Such a model allows us to study the properties of the neuron ensemble independently from the original data. It also permits to infer properties of the ensemble that cannot be directly obtained from the observed spike trains. The performance of the method is tested with spike trains artificially generated by a number of different neural networks.

Disentanglement of local field potential sources by independent component analysis

The spontaneous activity of working neurons yields synaptic currents that mix up in the volume conductor. This activity is picked up by intracerebral recording electrodes as local field potentials (LFPs), but their separation into original informative sources is an unresolved problem. Assuming that synaptic currents have stationary placing we implemented independent component model for blind source separation of LFPs in the hippocampal CA1 region. After suppressing contaminating sources from adjacent regions we obtained three main local LFP generators. The specificity of the information contained in isolated generators is much higher than in raw potentials as revealed by stronger phase-spike correlation with local putative interneurons. The spatial distribution of the population synaptic input corresponding to each isolated generator was disclosed by current-source density analysis of spatial weights. The found generators match with axonal terminal fields from subtypes of local interneurons and associational fibers from nearby subfields. The found distributions of synaptic currents were employed in a computational model to reconstruct spontaneous LFPs. The phase-spike correlations of simulated units and LFPs show laminar dependency that reflects the nature and magnitude of the synaptic currents in the targeted pyramidal cells. We propose that each isolated generator captures the synaptic activity driven by a different neuron subpopulation. This offers experimentally justified model of local circuits creating extracellular potential, which involves distinct neuron subtypes.

Schaffer-Specific Local Field Potentials Reflect Discrete Excitatory Events at Gamma Frequency That May Fire Postsynaptic Hippocampal CA1 Units

Information processing and exchange between brain nuclei are made through spike series sent by individual neurons in highly irregular temporal patterns. Synchronization in cell assemblies, proposed as a network language for internal neural representations, still has little experimental support. We use a novel technique to extract pathway-specific local field potentials (LFPs) in the hippocampus to explore the ongoing temporal structure of a single presynaptic input, the CA3 Schaffer pathway, and its contribution to the spontaneous output of CA1 units in anesthetized rat. We found that Schaffer-specific LFPs are composed of a regular succession of pulse-like excitatory packages initiated by spontaneous clustered firing of CA3 pyramidal cells to which individual units contribute variably. A fraction of these packages readily induce firing of CA1 pyramidal cells and interneurons, the so-called Schaffer-driven spikes, revealing the presynaptic origin in the output code of single CA1 units. The output of 70% of CA1 pyramidal neurons contains up to 10% of such spikes. Our results suggest a hierarchical internal operation of the CA3 region based on sequential oscillatory activation of pyramidal cell assemblies whose activity partly gets in the output code at the next station. We conclude that CA1 output may directly reflect the activity of specific ensembles of CA3 neurons. Thus, the fine temporal structure of pathway-specific LFPs, as an accurate readout of the activity of a presynaptic population, is useful in searching for hidden presynaptic code in irregular spikes series of individual neurons and assemblies.

Elements for a general memory structure: properties of recurrent neural networks used to form situation models

We study how individual memory items are stored assuming that situations given in the environment can be represented in the form of synaptic-like couplings in recurrent neural networks. Previous numerical investigations have shown that specific architectures based on suppression or max units can successfully learn static or dynamic stimuli (situations). Here we provide a theoretical basis concerning the learning process convergence and the network response to a novel stimulus. We show that, besides learning ”simple“ static situations, a nD network can learn and replicate a sequence of up to n different vectors or frames. We find limits on the learning rate and show coupling matrices developing during training in different cases including expansion of the network into the case of nonlinear interunit coupling. Furthermore, we show that a specific coupling matrix provides low-pass-filter properties to the units, thus connecting networks constructed by static summation units with continuous-time networks. We also show under which conditions such networks can be used to perform arithmetic calculations by means of pattern completion.

Spatial disorder and pattern formation in lattices of coupled bistable elements

Abstract The spatio-temporal dynamics of discrete lattices of coupled bistable elements is considered. It is shown that both regular and chaotic spatial field distributions can be realized depending on parameter values and initial conditions. For illustration, we provide results for two lattice systems: the FitzHugh-Nagumo model and a network of coupled bistable oscillators. For the latter we also prove the existence of phase clusters, with phase locking of elements in each cluster.

Cytoarchitectonic and Dynamic Origins of Giant Positive Local Field Potentials in the Dentate Gyrus

To determine why some pathways but not others produce sizable local field potentials (LFPs) and how far from the source can these be recorded, complementary experimental analyses and realistic modeling of specific brain structures are required. In the present study, we combined multiple in vivo linear recordings in rats and a tridimensional finite element model of the dentate gyrus, a curved structure displaying abnormally large positive LFPs. We demonstrate that the polarized dendritic arbour of granule cells (GCs), combined with the curved layered configuration of the population promote the spatial clustering of GC currents in the interposed hilus and project them through the open side at a distance from cell domains. LFPs grow up to 20 times larger than observed in synaptic sites. The dominant positive polarity of hilar LFPs was only produced by the synchronous activation of GCs in both blades by either somatic inhibition or dendritic excitation. Moreover, the corresponding anatomical pathways must project to both blades of the dentate gyrus as even a mild decrease in the spatial synchronization resulted in a dramatic reduction in LFP power in distant sites, yet not in the GC domains. It is concluded that the activation of layered structures may establish sharply delimited spatial domains where synaptic currents from one or another input appear to be segregated according to the topology of afferent pathways and the cytoarchitectonic features of the target population. These also determine preferred directions for volume conduction in the brain, of relevance for interpretation of surface EEG recordings.

Parallel Readout of Pathway-Specific Inputs to Laminated Brain Structures

Local field potentials (LFPs) capture the electrical activity produced by principal cells during integration of converging synaptic inputs from multiple neuronal populations. However, since synaptic currents mix in the extracellular volume, LFPs have complex spatiotemporal structure, making them hard to exploit. Here we propose a biophysical framework to identify and separate LFP-generators. First we use a computational multineuronal model that scales up single cell electrogenesis driven by several synaptic inputs to realistic aggregate LFPs. This approach relies on the fixed but distinct locations of synaptic inputs from different presynaptic populations targeting a laminated brain structure. Thus the LFPs are contributed by several pathway-specific LFP-generators, whose electrical activity is defined by the spatial distribution of synaptic terminals and the time course of synaptic currents initiated in target cells by the corresponding presynaptic population. Then we explore the efficacy of independent component analysis to blindly separate converging sources and reconstruct pathway-specific LFP-generators. This approach can optimally locate synaptic inputs with subcellular accuracy while the reconstructed time course of pathway-specific LFP-generators is reliable in the millisecond scale. We also describe few cases where the non-linear intracellular interaction of strongly overlapping LFP-generators may lead to a significant cross-contamination and the appearance of derivative generators. We show that the approach reliably disentangle ongoing LFPs in the hippocampus into contribution of several LFP-generators. We were able to readout in parallel the pathway-specific presynaptic activity of projection cells in the entorhinal cortex and pyramidal cells in the ipsilateral and contralateral CA3. Thus we provide formal mathematical and experimental support for parallel readout of the activity of converging presynaptic populations in working neuronal circuits from common LFPs.

Spatial Modules of Coherent Activity in Pathway-Specific LFPs in the Hippocampus Reflect Topology and Different Modes of Presynaptic Synchronization

Ongoing network activity often manifests as irregular fluctuations in local field potentials (LFPs), a complex mixture of multicellular synaptic currents of varying locations and extensions. Among other conditions, for synchronously firing presynaptic units to generate sizable postsynaptic LFPs, their axonal territories should overlap. We have taken advantage of anatomical regularity of the rat hippocampus and combined multiple linear recordings and spatial discrimination techniques to separate pathway-specific LFPs with enough spatial resolution to discriminate postsynaptic regions of varying activation, and to investigate their presynaptic origin, chemical nature, and spatial extension. We identified 6 main excitatory and inhibitory LFP generators with different synaptic territories in principal cells and hippocampal subfields matching anatomical pathways. Some recognized pathways did not contribute notably to LFPs. Each showed different septo-temporal spatial modules over which the field potential fluctuations were synchronous. These modules were explained by either the strong overlap of synaptic territories of coactivated afferent neurons (e.g., CA3 clusters for CA1 Schaffer LFPs), or widespread coalescence of postsynaptic territories (granule cell somatic inhibition). We also show evidence that distinct modes of afferent synchronization generate stereotyped spatial patterns of synchronous LFPs in one pathway. Thus, studying spatial coherence of pathway-specific LFPs provides remote access to the dynamics of afferent populations.