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 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.

Self-assembly of sensory neurons into ganglia-like microtissues

Unraveling intra- and inter-cellular signaling networks managing cell-fate control, coordinating complex differentiation regulatory circuits and shaping tissues and organs in living systems remain major challenges in the post-genomic era. Resting on the laurels of past-century monolayer culture technologies, the cell culture community has only recently begun to appreciate the potential of three-dimensional mammalian cell culture systems to reveal the full scope of mechanisms orchestrating the tissue-like cell quorum in space and time. Capitalizing on gravity-enforced self-assembly of monodispersed primary embryonic mouse cells in hanging drops, we designed and characterized a three-dimensional cell culture model for ganglion-like structures. Within 24h, a mixture of mouse embryonic fibroblasts (MEF) and cells, derived from the dorsal root ganglion (DRG) (sensory neurons and Schwann cells) grown in hanging drops, assembled to coherent spherical microtissues characterized by a MEF feeder core and a peripheral layer of DRG-derived cells. In a time-dependent manner, sensory neurons formed a polar ganglion-like cap structure, which coordinated guided axonal outgrowth and innervation of the distal pole of the MEF feeder spheroid. Schwann cells, present in embryonic DRG isolates, tended to align along axonal structures and myelinate them in an in vivo-like manner. Whenever cultivation exceeded 10 days, DRG:MEF-based microtissues disintegrated due to an as yet unknown mechanism. Using a transgenic MEF feeder spheroid, engineered for gaseous acetaldehyde-inducible interferon-beta (ifn-beta) production by cotransduction of retro-/ lenti-viral particles, a short 6-h ifn-beta induction was sufficient to rescue the integrity of DRG:MEF spheroids and enable long-term cultivation of these microtissues. In hanging drops, such microtissues fused to higher-order macrotissue-like structures, which may pave the way for sophisticated bottom-up tissue engineering strategies. DRG:MEF-based artificial micro- and macrotissue design demonstrated accurate key morphological aspects of ganglions and exemplified the potential of self-assembled scaffold-free multicellular micro-/macrotissues to provide new insight into organogenesis.

The impact of input fluctuations on the frequency-current relationships of layer 5 pyramidal neurons in the rat medial prefrontal cortex

The role of irregular cortical firing in neuronal computation is still debated, and it is unclear how signals carried by fluctuating synaptic potentials are decoded by downstream neurons. We examined in vitro frequency versus current (f-I) relationships of layer 5 (L5) pyramidal cells of the rat medial prefrontal cortex (mPFC) using fluctuating stimuli. Studies in the somatosensory cortex show that L5 neurons become insensitive to input fluctuations as input mean increases and that their f-I response becomes linear. In contrast, our results show that mPFC L5 pyramidal neurons retain an increased sensitivity to input fluctuations, whereas their sensitivity to the input mean diminishes to near zero. This implies that the discharge properties of L5 mPFC neurons are well suited to encode input fluctuations rather than input mean in their firing rates, with important consequences for information processing and stability of persistent activity at the network level.