THE RESONATE-AND-FIRE NEURON: TIME DEPENDENT AND FREQUENCY SELECTIVE NEURONS IN NEURAL NETWORKS

The means through which the nervous system perceives its environment is one of the most fascinating questions in contemporary science. Our endeavors to comprehend the principles of neural science provide an instance of how biological processes may inspire novel methods in mathematical modeling and engineering. The application ofmathematical models towards understanding neural signals and systems represents a vibrant field of research that has spanned over half a century. During this period, multiple approaches to neuronal modeling have been adopted, and each approach is adept at elucidating a specific aspect of nervous system function. Thus while bio-physical models have strived to comprehend the dynamics of actual physical processes occurring within a nerve cell, the phenomenological approach has conceived models that relate the ionic properties of nerve cells to transitions in neural activity. Further-more, the field of neural networks has endeavored to explore how distributed parallel processing systems may become capable of storing memory. Through this project, we strive to explore how some of the insights gained from biophysical neuronal modeling may be incorporated within the field of neural net-works. We specifically study the capabilities of a simple neural model, the Resonate-and-Fire (RAF) neuron, whose derivation is inspired by biophysical neural modeling. While reflecting further biological plausibility, the RAF neuron is also analytically tractable, and thus may be implemented within neural networks. In the following thesis, we provide a brief overview of the different approaches that have been adopted towards comprehending the properties of nerve cells, along with the framework under which our specific neuron model relates to the field of neuronal modeling. Subsequently, we explore some of the time-dependent neurocomputational capabilities of the RAF neuron, and we utilize the model to classify logic gates, and solve the classic XOR problem. Finally we explore how the resonate-and-fire neuron may be implemented within neural networks, and how such a network could be adapted through the temporal backpropagation algorithm.

The Role of Antennapedia in Anteroposterior Patterning of the Drosophila Melanogaster Ventral Nervous System

A major unresolved question in developmental neurobiology is how the nervous system is adapted to the specific needs of the organism at different life stages. In the holometabolous insect Drosophila melanogaster, the larval ventral nervous system (VNS) is comprised of similar repeating segments, as opposed to the adult VNS, which varies greatly from segment to segment both in number and types of neurons. The adult-specific neurons of each segment are generated by 25 distinct types of neuronal progenitor cells called neuroblasts (NBs) that appear in a stereotyped array (Truman et al., 2004). Each NB divides repeatedly to produce a distinct set of daughter cells termed a lineage, which is bilaterally symmetric but present to varying degrees in each segment. These daughter cells can be distinguished by their position within the nervous system as well as by their axonal projections. Each of the 25 NBs produces neurons; if both daughter cells are present in a lineage then both sibling populations survived, whereas if only one projection is seen cell death occurred, leaving a hemilineage (half lineage). In some lineages, the same sibling type survives in all segments in which the lineage appears, but in others, the surviving sibling type varies across segments, resulting in a different morphology for the same lineage in different segments. How are these differences in survival and morphology controlled? The Hox genes provide positional information for developing structures along the anterior-posterior (AP) axis of animals. They encode transcription factors, thereby controlling the activity of genes down stream. In the postembryonic VNS, each NB lineage features its own characteristic expression pattern of Hox genes Antp and Ubx, which can vary from segment-to-segment, and can thereby cause variation in the number of neural cells and axonal projections that survive. This study defines the wild-type expression pattern of Antp and elucidates the role of Antp in gain of function studies. These studies are possible due to the MARCM (Mosaic Analysis with a Repressible Cell Marker) method, which allows the genetically manipulated cells to be specifically labeled in an otherwise normal, unlabeled organism. The results indicate that Antp is expressed in a segment-, lineage-, and hemilineage-specific manner. Antp is sufficient for both anterior and posterior transformations of particular lineages, including promotion of cell death and/or survival as well as axon guidance.

The GABAB1b isoform mediates long-lasting inhibition of dendritic Ca2+ spikes in layer 5 somatosensory pyramidal neurons

The apical tuft of layer 5 pyramidal neurons is innervated by a large number of inhibitory inputs with unknown functions. Here, we studied the functional consequences and underlying molecular mechanisms of apical inhibition on dendritic spike activity. Extracellular stimulation of layer 1, during blockade of glutamatergic transmission, inhibited the dendritic Ca2+ spike for up to 400 ms. Activation of metabotropic GABAB receptors was responsible for a gradual and long-lasting inhibitory effect, whereas GABAA receptors mediated a short-lasting (approximately 150 ms) inhibition. Our results suggest that the mechanism underlying the GABAB inhibition of Ca2+ spikes involves direct blockade of dendritic Ca2+ channels. By using knockout mice for the two predominant GABAB1 isoforms, GABAB1a and GABAB1b, we showed that postsynaptic inhibition of Ca2+ spikes is mediated by GABAB1b, whereas presynaptic inhibition of GABA release is mediated by GABAB1a. We conclude that the molecular subtypes of GABAB receptors play strategically different physiological roles in neocortical neurons.

Multiple time scales of temporal response in pyramidal and fast spiking cortical neurons

Neural dynamic processes correlated over several time scales are found in vivo, in stimulus-evoked as well as spontaneous activity, and are thought to affect the way sensory stimulation is processed. Despite their potential computational consequences, a systematic description of the presence of multiple time scales in single cortical neurons is lacking. In this study, we injected fast spiking and pyramidal (PYR) neurons in vitro with long-lasting episodes of step-like and noisy, in-vivo-like current. Several processes shaped the time course of the instantaneous spike frequency, which could be reduced to a small number (1-4) of phenomenological mechanisms, either reducing (adapting) or increasing (facilitating) the neuron's firing rate over time. The different adaptation/facilitation processes cover a wide range of time scales, ranging from initial adaptation (<10 ms, PYR neurons only), to fast adaptation (<300 ms), early facilitation (0.5-1 s, PYR only), and slow (or late) adaptation (order of seconds). These processes are characterized by broad distributions of their magnitudes and time constants across cells, showing that multiple time scales are at play in cortical neurons, even in response to stationary stimuli and in the presence of input fluctuations. These processes might be part of a cascade of processes responsible for the power-law behavior of adaptation observed in several preparations, and may have far-reaching computational consequences that have been recently described.

Predicting spike timing of neocortical pyramidal neurons by simple threshold models

Neurons generate spikes reliably with millisecond precision if driven by a fluctuating current--is it then possible to predict the spike timing knowing the input? We determined parameters of an adapting threshold model using data recorded in vitro from 24 layer 5 pyramidal neurons from rat somatosensory cortex, stimulated intracellularly by a fluctuating current simulating synaptic bombardment in vivo. The model generates output spikes whenever the membrane voltage (a filtered version of the input current) reaches a dynamic threshold. We find that for input currents with large fluctuation amplitude, up to 75% of the spike times can be predicted with a precision of +/-2 ms. Some of the intrinsic neuronal unreliability can be accounted for by a noisy threshold mechanism. Our results suggest that, under random current injection into the soma, (i) neuronal behavior in the subthreshold regime can be well approximated by a simple linear filter; and (ii) most of the nonlinearities are captured by a simple threshold process.

GDNF family ligands display distinct action profiles on cultured GABAergic and serotonergic neurons of rat ventral mesencephalon

Glial-cell-line-derived neurotrophic factor (GDNF), neurturin (NRTN), artemin (ARTN) and persephin (PSPN), known as the GDNF family ligands (GFLs), influence the development, survival and differentiation of cultured dopaminergic neurons from ventral mesencephalon (VM). Detailed knowledge about the effects of GFLs on other neuronal populations in the VM is essential for their potential application as therapeutic molecules for Parkinson's disease. Hence, in a comparative study, we investigated the effects of GFLs on cell densities and morphological differentiation of gamma-aminobutyric acid-immunoreactive (GABA-ir) and serotonin-ir (5-HT-ir) neurons in primary cultures of E14 rat VM. We observed that all GFLs [10 ng/ml] significantly increased GABA-ir cell densities (1.6-fold) as well as neurite length/neuron. However, only GDNF significantly increased the number of primary neurites/neuron, and none of the GFLs affected soma size of GABA-ir neurons. In contrast, only NRTN treatment significantly increased 5-HT-ir cells densities at 10 ng/ml (1.3-fold), while an augmentation was seen for GDNF and PSPN at 100 ng/ml (2.4-fold and 1.7-fold, respectively). ARTN had no effect on 5-HT-ir cell densities. Morphological analysis of 5-HT-ir neurons revealed a significant increase of soma size, number of primary neurites/neuron and neurite length/neuron after GDNF exposure, while PSPN only affected soma size, and NRTN and ARTN failed to exert any effect. In conclusion, we identified GFLs as effective neurotrophic factors for VM GABAergic and serotonergic neurons, demonstrating characteristic individual action profiles emphasizing their important and distinct roles during brain development.