Daniel K. Wójcik

Classical and Quantum Fluctuation Theorems for Heat Exchange

The statistics of heat exchange between two classical or quantum finite systems initially prepared at different temperatures are shown to obey a fluctuation theorem.

Differential effects produced by ketamine on oscillatory activity recorded in the rat hippocampus, dorsal striatum and nucleus accumbens

Previously, we showed that NMDA antagonists enhance high-frequency oscillations (130–180 Hz) in the nucleus accumbens. However, whether NMDA antagonists can enhance high-frequency oscillations in other brain regions remains unclear. Here, we used monopolar, bipolar and inverse current source density techniques to examine oscillatory activity in the hippocampus, a region known to generate spontaneous ripples (∼200 Hz), its surrounding tissue, and the dorsal striatum, neuroanatomically related to the nucleus accumbens. In monopolar recordings, ketamine-induced increases in the power of high-frequency oscillations were detected in all structures, although the power was always substantially larger in the nucleus accumbens. In bipolar recordings, considered to remove common-mode input, high-frequency oscillations associated with ketamine injection were not present in the regions we investigated outside the nucleus accumbens. In line with this, inverse current source density showed the greatest changes in current to occur in the vicinity of the nucleus accumbens and a monopolar structure of the generator. We found little spatial localisation of ketamine high-frequency oscillations in other areas. In contrast, sharp-wave ripples, which were well localized to the hippocampus, occurred less frequently after ketamine. Notably, we also found ketamine produced small, but significant, changes in the power of 30–90 Hz gamma oscillations (an increase in the hippocampus and a decrease in the nucleus accumbens).

Inverse Current Source Density Method in Two Dimensions: Inferring Neural Activation from Multielectrode Recordings

The recent development of large multielectrode recording arrays has made it affordable for an increasing number of laboratories to record from multiple brain regions simultaneously. The development of analytical tools for array data, however, lags behind these technological advances in hardware. In this paper, we present a method based on forward modeling for estimating current source density from electrophysiological signals recorded on a two-dimensional grid using multi-electrode rectangular arrays. This new method, which we call two-dimensional inverse Current Source Density (iCSD 2D), is based upon and extends our previous one- and three-dimensional techniques. We test several variants of our method, both on surrogate data generated from a collection of Gaussian sources, and on model data from a population of layer 5 neocortical pyramidal neurons. We also apply the method to experimental data from the rat subiculum. The main advantages of the proposed method are the explicit specification of its assumptions, the possibility to include system-specific information as it becomes available, the ability to estimate CSD at the grid boundaries, and lower reconstruction errors when compared to the traditional approach. These features make iCSD 2D a substantial improvement over the approaches used so far and a powerful new tool for the analysis of multielectrode array data. We also provide a free GUI-based MATLAB toolbox to analyze and visualize our test data as well as user datasets.

Reward Learning Requires Activity of Matrix Metalloproteinase-9 in the Central Amygdala

Learning how to avoid danger and pursue reward depends on negative emotions motivating aversive learning and positive emotions motivating appetitive learning. The amygdala is a key component of the brain emotional system; however, an understanding of how various emotions are differentially processed in the amygdala has yet to be achieved. We report that matrix metalloproteinase-9 (MMP-9, extracellularly operating enzyme) in the central nucleus of the amygdala (CeA) is crucial for appetitive, but not for aversive, learning in mice. The knock-out of MMP-9 impairs appetitively motivated conditioning, but not an aversive one. MMP-9 is present at the excitatory synapses in the CeA with its activity greatly enhanced after the appetitive training. Finally, blocking extracellular MMP-9 activity with its inhibitor TIMP-1 provides evidence that local MMP-9 activity in the CeA is crucial for the appetitive, but not for aversive, learning.

Modelling and Analysis of Electrical Potentials Recorded in Microelectrode Arrays (MEAs)

Microelectrode arrays (MEAs), substrate-integrated planar arrays of up to thousands of closely spaced metal electrode contacts, have long been used to record neuronal activity in in vitro brain slices with high spatial and temporal resolution. However, the analysis of the MEA potentials has generally been mainly qualitative. Here we use a biophysical forward-modelling formalism based on the finite element method (FEM) to establish quantitatively accurate links between neural activity in the slice and potentials recorded in the MEA set-up. Then we develop a simpler approach based on the method of images (MoI) from electrostatics, which allows for computation of MEA potentials by simple formulas similar to what is used for homogeneous volume conductors. As we find MoI to give accurate results in most situations of practical interest, including anisotropic slices covered with highly conductive saline and MEA-electrode contacts of sizable physical extensions, a Python software package (ViMEAPy) has been developed to facilitate forward-modelling of MEA potentials generated by biophysically detailed multicompartmental neurons. We apply our scheme to investigate the influence of the MEA set-up on single-neuron spikes as well as on potentials generated by a cortical network comprising more than 3000 model neurons. The generated MEA potentials are substantially affected by both the saline bath covering the brain slice and a (putative) inadvertent saline layer at the interface between the MEA chip and the brain slice. We further explore methods for estimation of current-source density (CSD) from MEA potentials, and find the results to be much less sensitive to the experimental set-up.

Inverse Current-Source Density Method in 3D: Reconstruction Fidelity, Boundary Effects, and Influence of Distant Sources

Estimation of the continuous current-source density in bulk tissue from a finite set of electrode measurements is a daunting task. Here we present a methodology which allows such a reconstruction by generalizing the one-dimensional inverse CSD method. The idea is to assume a particular plausible form of CSD within a class described by a number of parameters which can be estimated from available data, for example a set of cubic splines in 3D spanned on a fixed grid of the same size as the set of measurements. To avoid specificity of particular choice of reconstruction grid we add random jitter to the points positions and show that it leads to a correct reconstruction. We propose different ways of improving the quality of reconstruction which take into account the sources located outside the recording region through appropriate boundary treatment. The efficiency of the traditional CSD and variants of inverse CSD methods is compared using several fidelity measures on different test data to investigate when one of the methods is superior to the others. The methods are illustrated with reconstructions of CSD from potentials evoked by stimulation of a bunch of whiskers recorded in a slab of the rat forebrain on a grid of 4×5×7 positions.

Time Evolution of Quantum Fractals

We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential, and free particle. The box-counting dimension of the probability density P(t)(x) = |Psi(x,t)|(2) is shown not to change during the time evolution. We prove a universal relation D(t) = 1+Dx/2 linking the dimensions of space cross sections Dx and time cross sections D(t) of the fractal quantum carpets.

Extracting functional components of neural dynamics with Independent Component Analysis and inverse Current Source Density

Local field potentials have good temporal resolution but are blurred due to the slow spatial decay of the electric field. For simultaneous recordings on regular grids one can reconstruct efficiently the current sources (CSD) using the inverse Current Source Density method (iCSD). It is possible to decompose the resultant spatiotemporal information about the current dynamics into functional components using Independent Component Analysis (ICA). We show on test data modeling recordings of evoked potentials on a grid of 4×5×7 points that meaningful results are obtained with spatial ICA decomposition of reconstructed CSD. The components obtained through decomposition of CSD are better defined and allow easier physiological interpretation than the results of similar analysis of corresponding evoked potentials in the thalamus. We show that spatiotemporal ICA decompositions can perform better for certain types of sources but it does not seem to be the case for the experimental data studied. Having found the appropriate approach to decomposing neural dynamics into functional components we use the technique to study the somatosensory evoked potentials recorded on a grid spanning a large part of the forebrain. We discuss two example components associated with the first waves of activation of the somatosensory thalamus. We show that the proposed method brings up new, more detailed information on the time and spatial location of specific activity conveyed through various parts of the somatosensory thalamus in the rat.

Common Atlas Format and 3D Brain Atlas Reconstructor: Infrastructure for Constructing 3D Brain Atlases

One of the challenges of modern neuroscience is integrating voluminous data of diferent modalities derived from a variety of specimens. This task requires a common spatial framework that can be provided by brain atlases. The first atlases were limited to two-dimentional presentation of structural data. Recently, attempts at creating 3D atlases have been made to offer navigation within non-standard anatomical planes and improve capability of localization of different types of data within the brain volume. The 3D atlases available so far have been created using frameworks which make it difficult for other researchers to replicate the results. To facilitate reproducible research and data sharing in the field we propose an SVG-based Common Atlas Format (CAF) to store 2D atlas delineations or other compatible data and 3D Brain Atlas Reconstructor (3dBAR), software dedicated to automated reconstruction of three-dimensional brain structures from 2D atlas data. The basic functionality is provided by (1) a set of parsers which translate various atlases from a number of formats into the CAF, and (2) a module generating 3D models from CAF datasets. The whole reconstruction process is reproducible and can easily be configured, tracked and reviewed, which facilitates fixing errors. Manual corrections can be made when automatic reconstruction is not sufficient. The software was designed to simplify interoperability with other neuroinformatics tools by using open file formats. The content can easily be exchanged at any stage of data processing. The framework allows for the addition of new public or proprietary content.

Generalized laminar population analysis (gLPA) for interpretation of multielectrode data from cortex

Laminar population analysis (LPA) is a method for analysis of electrical data recorded by linear multielectrodes passing through all lamina of cortex. Like principal components analysis (PCA) and independent components analysis (ICA), LPA offers a way to decompose the data into contributions from separate cortical populations. However, instead of using purely mathematical assumptions in the decomposition, LPA is based on physiological constraints, i.e., that the observed LFP (low-frequency part of signal) is driven by action-potential firing as observed in the MUA (multi-unit activity; high-frequency part of the signal). In the presently developed generalized laminar population analysis (gLPA) the set of basis functions accounting for the LFP data is extended compared to the original LPA, thus allowing for a better fit of the model to experimental data. This enhances the risk for overfitting, however, and we therefore tested various versions of gLPA on virtual LFP data in which we knew the ground truth. These synthetic data were generated by biophysical forward-modeling of electrical signals from network activity in the comprehensive, and well-known, thalamocortical network model developed by Traub and coworkers. The results for the Traub model imply that while the laminar components extracted by the original LPA method overall are in fair agreement with the ground-truth laminar components, the results may be improved by use of gLPA method with two (gLPA-2) or even three (gLPA-3) postsynaptic LFP kernels per laminar population.